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Malavazi AHA, Ahmadi B, Mazurek P, Mandarino A. Detuning effects for heat-current control in quantum thermal devices. Phys Rev E 2024; 109:064146. [PMID: 39020883 DOI: 10.1103/physreve.109.064146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2024] [Accepted: 06/06/2024] [Indexed: 07/20/2024]
Abstract
Navigating the intricacies of thermal management at the quantum scale is a challenge in the pursuit of advanced nanoscale technologies. To this extent, theoretical frameworks introducing minimal models mirroring the functionality of electronic current amplifiers and transistors, for instance, have been proposed. Different architectures of the subsystems composing a quantum thermal device can be considered, tacitly bringing drawbacks or advantages if properly engineered. This paper extends the prior research on thermotronics, studying a strongly coupled three-subsystem thermal device with a specific emphasis on a third excited level in the control subsystem. Our setup can be employed as a multipurpose device conditioned on the specific choice of internal parameters: heat switch, rectifier, stabilizer, and amplifier. The exploration of the detuned levels unveils a key role in the performance and working regime of the device. We observe a stable and strong amplification effect persisting over broad ranges of temperature. We conclude that considering a three-level system, as the one directly in contact with the control temperature, boosts output currents and the ability to operate our devices as a switch at various temperatures.
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Affiliation(s)
| | | | - Paweł Mazurek
- International Centre for Theory of Quantum Technologies, University of Gdańsk, Jana Bażyńskiego 1A, 80-309 Gdańsk, Poland
- Institute of Informatics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland
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Plyukhin AV. Nonergodic Brownian oscillator: High-frequency response. Phys Rev E 2023; 107:044107. [PMID: 37198800 DOI: 10.1103/physreve.107.044107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2023] [Accepted: 03/23/2023] [Indexed: 05/19/2023]
Abstract
We consider a Brownian oscillator whose coupling to the environment may lead to the formation of a localized normal mode. For lower values of the oscillator's natural frequency ω≤ω_{c}, the localized mode is absent and the unperturbed oscillator reaches thermal equilibrium. For higher values of ω>ω_{c} when the localized mode is formed, the unperturbed oscillator does not thermalize but rather evolves into a nonequilibrium cyclostationary state. We consider the response of such an oscillator to an external periodic force. Despite the coupling to the environment, the oscillator shows the unbounded resonance (with the response linearly increasing with time) when the frequency of the external force coincides with the frequency of the localized mode. An unusual resonance ("quasiresonance") occurs for the oscillator with the critical value of the natural frequency ω=ω_{c}, which separates thermalizing (ergodic) and nonthermalizing (nonergodic) configurations. In that case, the resonance response increases with time sublinearly, which can be interpreted as a resonance between the external force and the incipient localized mode.
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Affiliation(s)
- Alex V Plyukhin
- Department of Mathematics, Saint Anselm College, Manchester, New Hampshire 03102, USA
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Plyukhin AV. Nonergodic Brownian oscillator. Phys Rev E 2022; 105:014121. [PMID: 35193190 DOI: 10.1103/physreve.105.014121] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Accepted: 01/05/2022] [Indexed: 06/14/2023]
Abstract
We consider an open (Brownian) classical harmonic oscillator in contact with a non-Markovian thermal bath and described by the generalized Langevin equation. When the bath's spectrum has a finite upper cutoff frequency, the oscillator may have ergodic and nonergodic configurations. In ergodic configurations (when they exist, they correspond to lower oscillator frequencies) the oscillator demonstrates conventional relaxation to thermal equilibrium with the bath. In nonergodic configurations (which correspond to higher oscillator frequencies) the oscillator in general does not thermalize but relaxes to periodically correlated (cyclostationary) states whose statistics vary periodically in time. For a specific dissipation kernel in the Langevin equation, we evaluate explicitly relevant relaxation functions, which describe the evolution of mean values and time correlations. When the oscillator frequency is switched from a lower value to higher one, the oscillator may show parametric ergodic to nonergodic transitions with equilibrium initial and cyclostationary final states. These transitions are shown to resemble phase transitions of the second kind.
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Affiliation(s)
- Alex V Plyukhin
- Department of Mathematics, Saint Anselm College, Manchester, New Hampshire 03102, USA
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Gelin MF, Borrelli R, Chen L. Hierarchical Equations-of-Motion Method for Momentum System-Bath Coupling. J Phys Chem B 2021; 125:4863-4873. [PMID: 33929205 PMCID: PMC8279550 DOI: 10.1021/acs.jpcb.1c02431] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
For a broad class of quantum models of practical interest, we demonstrate that the Hamiltonian of the system nonlinearly coupled to a harmonic bath through the system and bath coordinates can be equivalently mapped into the Hamiltonian of the system bilinearly coupled to the bath through the system and bath momenta. We show that the Hamiltonian with bilinear system-bath momentum coupling can be treated by the hierarchical equations-of-motion (HEOM) method and present the corresponding proof-of-principle simulations. The developed methodology creates the opportunity to scrutinize a new family of nonlinear quantum systems by the numerically accurate HEOM method.
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Affiliation(s)
- Maxim F Gelin
- School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China
| | | | - Lipeng Chen
- Max Planck Institute for the Physics of Complex Systems, D-01187 Dresden, Germany
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Plyukhin AV. Non-Clausius heat transfer: The method of the nonstationary Langevin equation. Phys Rev E 2020; 102:052119. [PMID: 33327163 DOI: 10.1103/physreve.102.052119] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2020] [Accepted: 10/28/2020] [Indexed: 11/07/2022]
Abstract
Compared to other formulations of the second law of thermodynamics, the Clausius statement that heat does not spontaneously flow from cold to hot concerns a system in nonequilibrium states, and in that respect is more ambitious but also more ambiguous. We discuss two scenarios when the Clausius statement in its plain form does not hold. First, for ergodic systems, the energy transfer may be consistent with the statement on a coarse-grained timescale, but be anomalously directed during time intervals shorter than the thermalization time. In particular, when an initially colder system is brought in contact to a hotter bath, the internal energy of the former increases with time in a long run but not monotonically. Second, the heat transfer may not respect the Clausius statement on any timescale in nonergodic systems due to the formation of localized vibrational modes. We illustrate the two scenarios with a familiar model of an isotope atom attached to a semi-infinite harmonic atomic chain. Technically, the discussion is based on a Langevin equation for the isotope, using the initial condition when the isotope and chain are initially prepared in uncorrelated canonical states under the constraint that the boundary atom between the isotope and chain is initially fixed and later released. In such setting, the noise in the Langevin equation is nonstationary, and the fluctuation-dissipation relation has a nonstandard form.
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Grabert H, Thorwart M. Quantum mechanical response to a driven Caldeira-Leggett bath. Phys Rev E 2018; 98:012122. [PMID: 30110760 DOI: 10.1103/physreve.98.012122] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2018] [Indexed: 11/07/2022]
Abstract
We determine the frequency-dependent response characteristics of a quantum system to a driven Caldeira-Leggett bath. The bath degrees of freedom are explicitly driven by an external time-dependent force, in addition to the direct time-dependent forcing of the system itself. After general considerations of driven Caldeira-Leggett baths, we consider the Rubin model of a chain of quantum particles coupled by linear springs as an important model of a quantum dissipative system. We show that in the presence of time-dependent driving of the chain, this model can be mapped to a quantum system which couples to a driven Caldeira-Leggett bath. The effect of the bath driving is captured by a time-dependent force on the central system, which is, in principle, non-Markovian in nature. We study two specific examples, the exactly solvable case of a harmonic potential and a quantum two-state system for which we assume a weak system-bath coupling. We evaluate the dynamical response to a periodic driving of the system and the bath. The dynamic susceptibility is shown to be altered qualitatively by the bath drive: The dispersive part is enhanced at low frequencies and acquires a maximum at zero frequency. The absorptive part develops a shoulder-like behavior in this frequency regime. These features seem to be generic for quantum systems in a driven Caldeira-Leggett bath.
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Affiliation(s)
- Hermann Grabert
- Physikalisches Institut, Universität Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Michael Thorwart
- I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstraße 9, 20355 Hamburg, Germany.,Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
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Microscopic description for the emergence of collective dissipation in extended quantum systems. Sci Rep 2017; 7:42050. [PMID: 28176835 PMCID: PMC5296766 DOI: 10.1038/srep42050] [Citation(s) in RCA: 38] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2016] [Accepted: 01/05/2017] [Indexed: 11/08/2022] Open
Abstract
Practical implementations of quantum technology are limited by unavoidable effects of decoherence and dissipation. With achieved experimental control for individual atoms and photons, more complex platforms composed by several units can be assembled enabling distinctive forms of dissipation and decoherence, in independent heat baths or collectively into a common bath, with dramatic consequences for the preservation of quantum coherence. The cross-over between these two regimes has been widely attributed in the literature to the system units being farther apart than the bath's correlation length. Starting from a microscopic model of a structured environment (a crystal) sensed by two bosonic probes, here we show the failure of such conceptual relation, and identify the exact physical mechanism underlying this cross-over, displaying a sharp contrast between dephasing and dissipative baths. Depending on the frequency of the system and, crucially, on its orientation with respect to the crystal axes, collective dissipation becomes possible for very large distances between probes, opening new avenues to deal with decoherence in phononic baths.
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Nokkala J, Galve F, Zambrini R, Maniscalco S, Piilo J. Complex quantum networks as structured environments: engineering and probing. Sci Rep 2016; 6:26861. [PMID: 27230125 PMCID: PMC4882597 DOI: 10.1038/srep26861] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2016] [Accepted: 05/04/2016] [Indexed: 01/08/2023] Open
Abstract
We consider structured environments modeled by bosonic quantum networks and investigate the probing of their spectral density, structure, and topology. We demonstrate how to engineer a desired spectral density by changing the network structure. Our results show that the spectral density can be very accurately detected via a locally immersed quantum probe for virtually any network configuration. Moreover, we show how the entire network structure can be reconstructed by using a single quantum probe. We illustrate our findings presenting examples of spectral densities and topology probing for networks of genuine complexity.
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Affiliation(s)
- Johannes Nokkala
- Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014, Turun Yliopisto, Finland
| | - Fernando Galve
- IFISC (UIB-CSIC), Instituto de Fisica Interdisciplinary Sistemas Complejos, UIB Campus, 07122 Palma de Mallorca, Spain
| | - Roberta Zambrini
- IFISC (UIB-CSIC), Instituto de Fisica Interdisciplinary Sistemas Complejos, UIB Campus, 07122 Palma de Mallorca, Spain
| | - Sabrina Maniscalco
- Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014, Turun Yliopisto, Finland
| | - Jyrki Piilo
- Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014, Turun Yliopisto, Finland
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Abstract
We investigate Quantum Darwinism and the emergence of a classical world from the quantum one in connection with the spectral properties of the environment. We use a microscopic model of quantum environment in which, by changing a simple system parameter, we can modify the information back flow from environment into the system, and therefore its non-Markovian character. We show that the presence of memory effects hinders the emergence of classical objective reality, linking these two apparently unrelated concepts via a unique dynamical feature related to decoherence factors.
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Martinazzo R, Vacchini B, Hughes KH, Burghardt I. Communication: Universal Markovian reduction of Brownian particle dynamics. J Chem Phys 2011; 134:011101. [DOI: 10.1063/1.3532408] [Citation(s) in RCA: 88] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Martinazzo R, Hughes KH, Martelli F, Burghardt I. Effective spectral densities for system-environment dynamics at conical intersections: S2–S1 conical intersection in pyrazine. Chem Phys 2010. [DOI: 10.1016/j.chemphys.2010.08.010] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Helbig K, Just W, Radons G, Yang H. Dynamic structure factors and Lyapunov modes in disordered chains. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:026206. [PMID: 20866892 DOI: 10.1103/physreve.82.026206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2010] [Indexed: 05/29/2023]
Abstract
We investigate various dynamic structure factors for harmonic and anharmonic chains. For harmonic chains with mass disorder we find some unexpected features, such as a fine structure contributing to a central peak, which is present also in the spatial spectra of the eigenfunctions. These results are contrasted with structure factors of Lyapunov modes obtained for the disordered Lennard-Jones chain. For this nonlinear system the static and the dynamic Lyapunov structure factors show opposite trends in their temperature dependence.
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Affiliation(s)
- Kai Helbig
- Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany
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Morgado WAM, Soares-Pinto DO. Exact time-averaged thermal conductance for small systems: comparison between direct calculation and Green-Kubo formalism. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:051116. [PMID: 19518425 DOI: 10.1103/physreve.79.051116] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2009] [Revised: 04/08/2009] [Indexed: 05/27/2023]
Abstract
In this paper, we study exactly the thermal conductance for a low dimensional system represented by two coupled massive Brownian particles, both directly and via a Green-Kubo expression. Both approaches give exactly the same result. We also obtain exactly the steady-state probability distribution for that system by means of time averaging.
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Affiliation(s)
- W A M Morgado
- Departamento de Física, Pontifícia Universidade Católica, National Institute of Science and Technology for Complex Systems, 22452-970 Rio de Janeiro, RJ, Brazil.
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Tamura H, Bittner ER, Burghardt I. Nonadiabatic quantum dynamics based on a hierarchical electron-phonon model: Exciton dissociation in semiconducting polymers. J Chem Phys 2007; 127:034706. [PMID: 17655454 DOI: 10.1063/1.2748050] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A hierarchical electron-phonon coupling model is applied to describe the ultrafast decay of a photogenerated exciton at a donor-acceptor polymer heterojunction, via a vibronic coupling mechanism by which a charge-localized interfacial state is created. Expanding upon an earlier Communication [H. Tamura et al., J. Chem. Phys. 126, 021103 (2007)], we present a quantum dynamical analysis based on a two-state linear vibronic coupling model, which accounts for a two-band phonon bath including high-frequency C[Double Bond]C stretch modes and low-frequency ring torsional modes. Building upon this model, an analysis in terms of a hierarchical chain of effective modes is carried out, whose construction is detailed in the present paper. Truncation of this chain at the order n (i.e., 3n+3 modes) conserves the Hamiltonian moments (cumulants) up to the (2n+3)rd order. The effective-mode analysis highlights (i) the dominance of the high-frequency modes in the coupling to the electronic subsystem and (ii) the key role of the low-frequency modes in the intramolecular vibrational redistribution process that is essential in mediating the decay to the charge-localized state. Due to this dynamical interplay, the effective-mode hierarchy has to be carried beyond the first order in order to obtain a qualitatively correct picture of the nonadiabatic process. A reduced model of the dynamics, including a Markovian closure of the hierarchy, is presented. Dynamical calculations were carried out using the multiconfiguration time-dependent Hartree method.
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Affiliation(s)
- Hiroyuki Tamura
- Département de Chimie, Ecole Normale Supérieure, 24 Rue Lhomond, F-75231 Paris Cedex 05, France.
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Zerbe C, Hänggi P. Brownian parametric quantum oscillator with dissipation. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:1533-1543. [PMID: 9963574 DOI: 10.1103/physreve.52.1533] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Wilson R, Chu-Ko B. Study of harmonic crystal momentum autocorrelation and fluctuation functions. Chem Phys Lett 1988. [DOI: 10.1016/0009-2614(88)85163-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Calzetta E, Hu BL. Nonequilibrium quantum fields: Closed-time-path effective action, Wigner function, and Boltzmann equation. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1988; 37:2878-2900. [PMID: 9958563 DOI: 10.1103/physrevd.37.2878] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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20
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Greer WL, Haus JW. Electronic Green’s function for a linear crystal in a thermal gradient. J Chem Phys 1978. [DOI: 10.1063/1.436290] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Greer WL. Nonequilibrium force fluctuations in an isotopically impure linear harmonic crystal. J Chem Phys 1974. [DOI: 10.1063/1.1681855] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Cukier RI, Wheeler JC. Time autocorrelation functions for harmonic solids from Gaussian quadratures. J Chem Phys 1974. [DOI: 10.1063/1.1680961] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Broadhurst MG, Mopsik FI. Normal Mode Calculation of Grüneisen Thermal Expansion in n‐Alkanes. J Chem Phys 1971. [DOI: 10.1063/1.1674666] [Citation(s) in RCA: 34] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Park YRL, Tahk CT, Wilson DJ. Quantum Dynamics of Anharmonic Oscillators by Numerical Integration. J Chem Phys 1970. [DOI: 10.1063/1.1674059] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Allen KR, Ford J. Lattice Thermal Conductivity for a One-Dimensional, Harmonic, Isotopically Disordered Crystal. ACTA ACUST UNITED AC 1968. [DOI: 10.1103/physrev.176.1046] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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