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Bhattacharyya S, Ghosh A, Ray DS. Microscopic quantum generalization of classical Liénard oscillators. Phys Rev E 2021; 103:012118. [PMID: 33601547 DOI: 10.1103/physreve.103.012118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Accepted: 12/28/2020] [Indexed: 11/07/2022]
Abstract
Based on a system-reservoir model and an appropriate choice of nonlinear coupling, we have explored the microscopic quantum generalization of classical Liénard systems. Making use of oscillator coherent states and canonical thermal distributions of the associated c numbers, we have derived the quantum Langevin equation of the reduced system which admits single or multiple limit cycles. It has been shown that detailed balance in the form of the fluctuation-dissipation relation preserves the dynamical stability of the attractors even in the case of vacuum excitation. The quantum versions of Rayleigh, van der Pol, and several other variants of Liénard oscillators are derived as special cases in our theoretical scheme within a mean-field description.
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Affiliation(s)
| | - Arnab Ghosh
- Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
| | - Deb Shankar Ray
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
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Jang S. Generalized quantum Fokker-Planck equation for photoinduced nonequilibrium processes with positive definiteness condition. J Chem Phys 2016; 144:214102. [PMID: 27276940 DOI: 10.1063/1.4952477] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Abstract
This work provides a detailed derivation of a generalized quantum Fokker-Planck equation (GQFPE) appropriate for photo-induced quantum dynamical processes. The path integral method pioneered by Caldeira and Leggett (CL) [Physica A 121, 587 (1983)] is extended by utilizing a nonequilibrium influence functional applicable to different baths for the ground and the excited electronic states. Both nonequilibrium and non-Markovian effects are accounted for consistently by expanding the paths in the exponents of the influence functional up to the second order with respect to time. This procedure results in approximations involving only single time integrations for the exponents of the influence functional but with additional time dependent boundary terms that have been ignored in previous works. The boundary terms complicate the derivation of a time evolution equation but do not affect position dependent physical observables or the dynamics in the steady state limit. For an effective density operator with the boundary terms factored out, a time evolution equation is derived, through short time expansion of the effective action and Gaussian integration in analytically continued complex domain of space. This leads to a compact form of the GQFPE with time dependent kernels and additional terms, which renders the resulting equation to be in the Dekker form [Phys. Rep. 80, 1 (1981)]. Major terms of the equation are analyzed for the case of Ohmic spectral density with Drude cutoff, which shows that the new GQFPE satisfies the positive definiteness condition in medium to high temperature limit. Steady state limit of the GQFPE is shown to approach the well-known expression derived by CL in the high temperature and Markovian bath limit and also provides additional corrections due to quantum and non-Markovian effects of the bath.
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Affiliation(s)
- Seogjoo Jang
- Department of Chemistry and Biochemistry, Queens College, City University of New York, 65-30 Kissena Boulevard, Queens, New York 11367, USA and Ph.D. Programs in Chemistry and Physics, and Initiative for Theoretical Sciences, Graduate Center, City University of New York, 365 Fifth Avenue, New York, New York 10016, USA
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Ray S, Bag BC. Shannon entropic temperature and its lower and upper bounds for non-Markovian stochastic dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032103. [PMID: 25314391 DOI: 10.1103/physreve.90.032103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2014] [Indexed: 06/04/2023]
Abstract
In this article we have studied Shannon entropic nonequilibrium temperature (NET) extensively for a system which is coupled to a thermal bath that may be Markovian or non-Markovian in nature. Using the phase-space distribution function, i.e., the solution of the generalized Fokker Planck equation, we have calculated the entropy production, NET, and their bounds. Other thermodynamic properties like internal energy of the system, heat, and work, etc. are also measured to study their relations with NET. The present study reveals that the heat flux is proportional to the difference between the temperature of the thermal bath and the nonequilibrium temperature of the system. It also reveals that heat capacity at nonequilibrium state is independent of both NET and time. Furthermore, we have demonstrated the time variations of the above-mentioned and related quantities to differentiate between the equilibration processes for the coupling of the system with the Markovian and the non-Markovian thermal baths, respectively. It implies that in contrast to the Markovian case, a certain time is required to develop maximum interaction between the system and the non-Markovian thermal bath (NMTB). It also implies that longer relaxation time is needed for a NMTB compared to a Markovian one. Quasidynamical behavior of the NMTB introduces an oscillation in the variation of properties with time. Finally, we have demonstrated how the nonequilibrium state is affected by the memory time of the thermal bath.
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Affiliation(s)
- Somrita Ray
- Department of Chemistry, Visva-Bharati, Santiniketan 731 235, India
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Shit A, Chattopadhyay S, Chaudhuri JR. Quantum stochastic dynamics in the presence of a time-periodic rapidly oscillating potential: nonadiabatic escape rate. J Phys Chem A 2013; 117:8576-90. [PMID: 23627350 DOI: 10.1021/jp402565y] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Escape from a metastable state in the presence of a high-frequency field (where the driving becomes nonadiabatic) underlies a broad range of phenomena of physics and chemistry, and thus its understanding is of paramount importance. We study the problem of intermediate-to-high-damping escape from a metastable state of a dissipative system driven by a rapidly oscillating field, one of the most important classes of nonequilibrium systems, in a broad range of field driving frequencies (ω) and amplitudes (a). We construct a Langevin equation using quantum gauge transformation in the light of Floquet theorem and exploiting a systematic perturbative expansion in powers of 1/ω using "Kapitza-Landau time window". The quantum dynamics in a high-frequency field are found to be described by an effective time-independent potential. The temperature dependence of escape rate and the change of its form with varying parameters of the field have been analyzed. It may decrease upon increasing the temperature which is contingent on the effects of intricate interplay between external modulation and dissipation. The crossover temperature between tunnelling and thermal hopping increases with an increase in external modulation so that quantum effects in the escape are relevant at higher temperatures. These observations are uncommon and counterintuitive and, therefore, of considerable interest. Our results might be valuable for the exploration of the dynamics of cold atoms in electromagnetic fields.
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Affiliation(s)
- Anindita Shit
- Department of Chemistry, Bengal Engineering and Science University , Shibpur, Howrah 711103, India
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Ghosh A, Sinha SS, Ray DS. Canonical formulation of quantum dissipation and noise in a generalized spin bath. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:011122. [PMID: 23005383 DOI: 10.1103/physreve.86.011122] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2012] [Indexed: 06/01/2023]
Abstract
The quantum dynamics of a particle coupled to the dissipative degrees of freedom of a generalized spin bath in the presence of an external force field is presented. Based on Holstein-Primakoff transformation, which sets up a mapping between boson and spin operators, we show that the spin-1/2 bath and the harmonic bath can be realized as two special limits of the generalized bath. In the large spin limit, the Hamiltonian reduces to well-known Zwanzig Hamiltonian. Making use of spin coherent states and canonical thermal distributions of the associated c numbers, we derive and explore the quantum Langevin equation and the properties of the spin and harmonic baths in the context of quantum dissipation of the system.
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Affiliation(s)
- Arnab Ghosh
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
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Ghosh A, Sinha SS, Ray DS. Fermionic oscillator in a fermionic bath. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:011138. [PMID: 23005399 DOI: 10.1103/physreve.86.011138] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2012] [Revised: 06/15/2012] [Indexed: 06/01/2023]
Abstract
The quantum dissipation of a fermionic oscillator in an environment of fermionic oscillators is considered. Since fermions anticommute, their eigenvalues are anticommuting numbers. Based on an expansion of the reduced density operator in terms of fermionic coherent states which make use of these anticommuting numbers or Grassmann variables, a Fokker-Planck equation for the associated quasiprobability distribution function is derived. The density operator approach to fermionic fields as introduced by Cahill and Glauber [Phys. Rev. A 59, 1538 (1999)] thus can be extended to the nonequilibrium domain.
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Affiliation(s)
- Arnab Ghosh
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
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Shit A, Chattopadhyay S, Chaudhuri JR. Enhancement of transport properties of a Brownian particle due to quantum effects: Smoluchowski limit. Chem Phys 2012. [DOI: 10.1016/j.chemphys.2011.12.011] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Sinha SS, Ghosh A, Ray DS. Decay of a metastable state induced by a spin bath. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:041113. [PMID: 22181093 DOI: 10.1103/physreve.84.041113] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2011] [Indexed: 05/31/2023]
Abstract
The spin-bath induced decay of a quantum system out of a metastable state, which can tunnel and undergo thermal activation, is considered. The treatment is based on the c-number description of bath degrees of freedom and a canonical thermal distribution of the associated c-number variables. We show that, apart from the usual frequency prefactor and its dynamical modification in the spatial diffusion-limited regime, i.e., the Grote-Hynes factor, the rate coefficient contains two other factors. One is a quantum correction to the dynamical factor resulting from quantum transmission and reflection of the particle at the finite barrier. This term exhibits exponential rate enhancement at low temperature. The other one is a quantum corrected Arrhenius factor, which incorporates the effect of thermal saturation. At 0 K, dissipation due to tunneling multiplies the tunneling probability by a factor that gets exponentially damped by friction, implying that, at this temperature, the behavior of spin bath is almost identical to that of a harmonic bath.
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Ghosh A, Sinha SS, Ray DS. Dissipation in a spin bath: thermally induced coherent intensity and spectral splitting. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:061154. [PMID: 21797349 DOI: 10.1103/physreve.83.061154] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2011] [Revised: 05/11/2011] [Indexed: 05/31/2023]
Abstract
We have explored the role of dissipation in the scattered intensity and spectrum of resonance fluorescence from an excited two-level system in a spin bath. It has been shown that depending on the field strength a crossover temperature sets up a boundary between the coherent and incoherent intensity regimes, and at low field the scattered intensity may be coherent even at high temperature. We demonstrate the formation of a thermally induced Mollow triplet in the low-field regime.
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Affiliation(s)
- Arnab Ghosh
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata, India
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Baura A, Sen MK, Goswami G, Bag BC. Colored non-Gaussian noise driven open systems: Generalization of Kramers’ theory with a unified approach. J Chem Phys 2011; 134:044126. [DOI: 10.1063/1.3521394] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Sinha SS, Mondal D, Bag BC, Ray DS. Quantum diffusion in a fermionic bath. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:051125. [PMID: 21230455 DOI: 10.1103/physreve.82.051125] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2010] [Indexed: 05/30/2023]
Abstract
We propose a scheme for quantum brownian motion of a particle in a fermionic bath. Based on the spin coherent-state representation of the noise operators and a canonical thermal distribution of the associated c numbers, we derive a quantum analog of generalized Langevin equation for quantum-mechanical mean position of the particle subjected to an external force field. The approach allows us to map the quantum problem on a classical setting. The quantum dispersion around the mean can be estimated order by order by a set of quantum correction equations up to a desired degree of accuracy for a given nonlinear potential. We derive a quantum diffusion equation for free particle and show that quantization, in general, enhances the mean-square displacement. Increase in temperature leads to suppression of mean-square displacement. The method is based on canonical quantization procedure and may be used for understanding diffusive transport and thermally activated processes in a fermionic bath.
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Ghosh P, Shit A, Chattopadhyay S, Chaudhuri JR. External-noise-driven bath and the generalized semiclassical Kramers theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:041113. [PMID: 21230244 DOI: 10.1103/physreve.82.041113] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2010] [Revised: 08/19/2010] [Indexed: 05/30/2023]
Abstract
We address the issue of a system that has been tacitly made thermodynamically open by externally driving the associated heat bath in an attempt to gain better insight regarding many physical situations that are akin to this problem. This work embodies the study of the quantum effects in the rate of decay from a metastable state of a Brownian particle which is in contact with a correlated noise-driven bath. We do this by initiating from a suitable system-reservoir model to derive the operator-valued Langevin equation. This further leads us to the corresponding c-number analog that includes quantum effects in leading order. Suitable mathematical treatment culminates in the quantum Fokker-Planck equation, the solution to which yields the rate expression. Finally, we put this to thorough numerical analysis.
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Affiliation(s)
- Pradipta Ghosh
- Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India
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Ghosh P, Chattopadhyay S, Chaudhuri JR. Stochastic resonance in a generalized quantum Kubo oscillator. J Phys Chem B 2010; 114:1368-79. [PMID: 20041674 DOI: 10.1021/jp909858c] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We discuss stochastic resonance in a biased linear quantum system that is subject to multiplicative and additive noises. Starting from a microscopic system-reservoir Hamiltonian, we derive a c-number analogue of the generalized Langevin equation. The developed approach puts forth a quantum mechanical generalization of the "Kubo type" oscillator which is a linear system. Such a system is often used in the literature to study various phenomena in nonequilibrium systems via a particular interaction between system and the external noise. Our analytical results proposed here have the ability to reveal the role of external noise and vis-a-vis the mechanisms and detection of subtle underlying signatures of the stochastic resonance behavior in a linear system. In our development, we show that only when the external noise possesses a "finite correlation time" the quantum effect begins to appear. We observe that the quantum effect enhances the resonance in comparison to the classical one.
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Affiliation(s)
- Pradipta Ghosh
- Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India
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Yilmaz B, Ayik S, Abe Y, Boilley D. Non-Markovian diffusion over a parabolic potential barrier: Influence of the friction-memory function. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:011121. [PMID: 18351832 DOI: 10.1103/physreve.77.011121] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2007] [Revised: 11/16/2007] [Indexed: 05/26/2023]
Abstract
The over-passing probability across an inverted parabolic potential barrier is investigated according to the classical and quantal generalized Langevin equations. It is shown that, in the classical case, the asymptotic value of the over-passing probability is determined by a single dominant root of the "characteristic function," and it is given by a simple expression. The expression for the over-passing probability is quite general, and details of dissipation mechanism and memory effects enter into the expression only through the dominant root of the characteristic equation.
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Affiliation(s)
- B Yilmaz
- Physics Department, Ankara University, 06100 Ankara, Turkey
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Bag BC, Hu CK. Escape through an unstable limit cycle: resonant activation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:061107. [PMID: 16906809 DOI: 10.1103/physreve.73.061107] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2006] [Indexed: 05/11/2023]
Abstract
We consider a Brownian particle acted on by a linear conservative force, a nonlinear frictional force, and multiplicative colored and additive white noises; the frictional force can be negative when the external energy supply is large enough. We numerically calculate the mean first passage time (MFPT) for the particle to escape from an unstable limit cycle and find resonant activation, i.e., the MFPT first decreases, followed by a rise after passing through a minimum with increasing noise correlation time tau for a fixed noise variance. For fixed noise strength of the multiplicative noise the MFPT increases linearly with tau. This is in sharp contrast to the case of fluctuations of nonlinear potentials, in which the MFPT first increases nonlinearly before reaching a limiting value. Our model could be useful for understanding some biological processes.
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Ghosh PK, Ray DS. Stochastic energetics of quantum transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:036103. [PMID: 16605594 DOI: 10.1103/physreve.73.036103] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2005] [Indexed: 05/08/2023]
Abstract
We examine the stochastic energetics of directed quantum transport due to rectification of nonequilibrium thermal fluctuations. We calculate the quantum efficiency of a ratchet device both in presence and absence of an external load to characterize two quantifiers of efficiency. It has been shown that the quantum current as well as efficiency in absence of load (Stokes efficiency) is higher as compared to classical current and efficiency, respectively, at low temperature. The conventional efficiency of the device in presence of load on the other hand is higher for a classical system in contrast to its classical counterpart. The maximum conventional efficiency being independent of the nature of the bath and the potential remains the same for classical and quantum systems.
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Affiliation(s)
- Pulak Kumar Ghosh
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
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Ghosh PK, Barik D, Bag BC, Ray DS. Quantum escape kinetics over a fluctuating barrier. J Chem Phys 2005; 123:224104. [PMID: 16375467 DOI: 10.1063/1.2135781] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The escape rate of a particle over a fluctuating barrier in a double-well potential exhibits resonance at an optimum value of correlation time of fluctuation. This has been shown to be important in several variants of kinetic model of chemical reactions. We extend the analysis of this phenomenon of resonant activation to quantum domain to show how quantization significantly enhances resonant activation at low temperature due to tunneling.
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Affiliation(s)
- Pulak Kumar Ghosh
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
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Ghosh PK, Barik D, Ray DS. Noise-induced quantum transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:041107. [PMID: 15903657 DOI: 10.1103/physreve.71.041107] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2005] [Indexed: 05/02/2023]
Abstract
We analyze the problem of directed quantum transport induced by external exponentially correlated telegraphic noise. In addition to quantum nature of the heat bath, nonlinearity of the periodic system potential brings in quantum contribution. We observe that quantization, in general, enhances classical current at low temperature, while the differences become insignificant at higher temperature. Interplay of quantum diffusion and quantum correction to system potential is analyzed for various ranges of temperature, correlation time and strength of external noise and asymmetry parameters. A possible experimental realization of the observed quantum effects in a superionic conductor placed in a random asymmetric dichotomous electric field has been suggested.
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Affiliation(s)
- Pulak Kumar Ghosh
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
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Bolivar AO. Quantum tunneling at zero temperature in the strong friction regime. PHYSICAL REVIEW LETTERS 2005; 94:026807. [PMID: 15698213 DOI: 10.1103/physrevlett.94.026807] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2004] [Indexed: 05/24/2023]
Abstract
In the large damping limit we derive a Fokker-Planck equation in configuration space (the so-called Smoluchowski equation) describing a Brownian particle immersed into a thermal environment and subjected to a nonlinear external force. We quantize this stochastic system and survey the problem of escape over a double-well potential barrier. Our finding is that the quantum Kramers rate does not depend on the friction coefficient at low temperatures; i.e., we predict a superfluidity phenomenon in overdamped open systems. Moreover, at zero temperature we show that the quantum escape rate does not vanish in the strong friction regime. This result, therefore, is in contrast with the work by Ankerhold et al. [Phys. Rev. Lett. 87, 086802 (2001)]] in which no quantum tunneling is predicted at zero temperature.
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Affiliation(s)
- A O Bolivar
- Instituto Cultural Eudoro de Sousa, Grupo Mário Schönberg de Estudos em Física-Matemática-Filosofia, Ceilândia, 72225-971, Cx. P. 7316, D.F, Brazil
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Barik D, Ray DS. Anharmonic quantum contribution to vibrational dephasing. J Chem Phys 2004; 121:1681-9. [PMID: 15260719 DOI: 10.1063/1.1766007] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Based on a quantum Langevin equation and its corresponding Hamiltonian within a c-number formalism we calculate the vibrational dephasing rate of a cubic oscillator. It is shown that leading order quantum correction due to anharmonicity of the potential makes a significant contribution to the rate and the frequency shift. We compare our theoretical estimates with those obtained from experiments for small diatomics N(2), O(2), and CO.
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Affiliation(s)
- Debashis Barik
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
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Banerjee D, Bag BC, Banik SK, Ray DS. Solution of quantum Langevin equation: Approximations, theoretical and numerical aspects. J Chem Phys 2004; 120:8960-72. [PMID: 15267831 DOI: 10.1063/1.1711593] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Based on a coherent state representation of noise operator and an ensemble averaging procedure using Wigner canonical thermal distribution for harmonic oscillators, a generalized quantum Langevin equation has been recently developed [Phys. Rev. E 65, 021109 (2002); 66, 051106 (2002)] to derive the equations of motion for probability distribution functions in c-number phase-space. We extend the treatment to explore several systematic approximation schemes for the solutions of the Langevin equation for nonlinear potentials for a wide range of noise correlation, strength and temperature down to the vacuum limit. The method is exemplified by an analytic application to harmonic oscillator for arbitrary memory kernel and with the help of a numerical calculation of barrier crossing, in a cubic potential to demonstrate the quantum Kramers' turnover and the quantum Arrhenius plot.
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Affiliation(s)
- Dhruba Banerjee
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
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Majee P, Bag BC. The effect of interference of coloured additive and multiplicative white noises on escape rate. ACTA ACUST UNITED AC 2004. [DOI: 10.1088/0305-4470/37/10/003] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Barik D, Bag BC, Ray DS. Numerical simulation of transmission coefficient using c-number Langevin equation. J Chem Phys 2003. [DOI: 10.1063/1.1628227] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Barik D, Banik SK, Ray DS. Quantum phase-space function formulation of reactive flux theory. J Chem Phys 2003. [DOI: 10.1063/1.1579473] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Banerjee D, Banik SK, Bag BC, Ray DS. Quantum Kramers equation for energy diffusion and barrier crossing dynamics in the low-friction regime. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:051105. [PMID: 12513465 DOI: 10.1103/physreve.66.051105] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2002] [Indexed: 05/24/2023]
Abstract
Based on a true phase space probability distribution function and an ensemble averaging procedure we have recently developed [Phys. Rev. E 65, 021109 (2002)] a non-Markovian quantum Kramers equation to derive the quantum rate coefficient for barrier crossing due to thermal activation and tunneling in the intermediate to strong friction regime. We complement and extend this approach to weak friction regime to derive quantum Kramers equation in energy space and the rate of decay from a metastable well. The theory is valid for arbitrary temperature and noise correlation. We show that depending on the nature of the potential there may be a net reduction of the total quantum rate below its corresponding classical value, which is in conformity with earlier observation. The method is independent of path integral approaches and takes care of quantum effects to all orders.
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Affiliation(s)
- Dhruba Banerjee
- Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700 032, India
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Bihary Z, Chaban GM, Gerber RB. Stability of a chemically bound helium compound in high-pressure solid helium. J Chem Phys 2002. [DOI: 10.1063/1.1506150] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Banik SK, Bag BC, Ray DS. Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:051106. [PMID: 12059528 DOI: 10.1103/physreve.65.051106] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2001] [Revised: 02/20/2002] [Indexed: 05/23/2023]
Abstract
Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).
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Affiliation(s)
- Suman Kumar Banik
- Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700 032, India
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