Non-Markovian dynamics of quantum systems. I. Formalism and transport coefficients

Orbital diamagnetism of two-dimensional quantum systems in a dissipative environment: Non-Markovian effect and application to graphene

The non-Markovian dynamics of a charged particle confined in the harmonic oscillator and linearly coupled to a neutral bosonic heat bath is investigated in the external uniform magnetic field. The analytical expressions are derived for the time-dependent and asymptotic orbital angular momenta. The transition from non-Markovian dynamics to Markovian dynamics and the transition from a confined charge particle to a free charge particle are considered. The orbital diamagnetism of graphene in a dissipative environment and an external uniform magnetic field is studied and compared with existing experimental data. The results are presented for the electric conductivity and resonance behavior of the mass magnetization in graphene.

Non-Markovian dynamics of quantum systems coupled with several mixed fermionic-bosonic heat baths

For the fermionic or bosonic oscillator fully coupled to several heat baths with mixed statistics, the analytical expressions for the occupation numbers are derived within the non-Markovian quantum Langevin approach. Employing two or three heat baths and the Ohmic dissipation with Lorenzian cutoffs, the role of statistics of the system and heat baths in the dynamics of the system is studied.

Non-Markovian dynamics of fermionic and bosonic systems coupled to several heat baths

Employing the fermionic and bosonic Hamiltonians for the collective oscillator linearly FC-coupled with several heat baths, the analytical expressions for the collective occupation number are derived within the non-Markovian quantum Langevin approach. The master equations for the occupation number of collective subsystem are derived and discussed. In the case of Ohmic dissipation with Lorenzian cutoffs, the possibility of reduction of the system with several heat baths to the system with one heat bath is analytically demonstrated. For the fermionic and bosonic systems, a comparative analysis is performed between the collective subsystem coupled to two heat baths and the reference case of the subsystem coupled to one bath.

Non-Markovian dynamics of an open quantum system with nonstationary coupling

The spectral, dissipative, and statistical properties of the damped quantum oscillator are studied in the case of non-Markovian and nonstationary system-heat bath coupling. The dissipation of collective energy is shown to be slowed down, and the decoherence rate and entropy grow with modulation frequency.

Dissipative stochastic mechanics for capturing neuronal dynamics under the influence of ion channel noise: formalism using a special membrane

Based on the idea conveyed in the author's prior study [Fluct. Noise Lett. 6, L147 (2006)], a physical approach for the description of neuronal dynamics under the influence of ion channel noise is developed in the realm of Nelson's stochastic mechanics when open to dissipative environments. The formalism therein is scrutinized using a special membrane with some tailored properties giving the Rose-Hindmarsh dynamics in the deterministic limit. Led by the presence of multiple number of gates in an ion channel, a dual viewpoint of channel noise is established. Then, stochastic mechanics is adopted to model those channel fluctuations emerging from the uncertainty in accessing the permissible topological states of open gates. A mutual interaction between the above fluctuations and the noise, emerging from the stochasticity in the movement of gating particles between the inner and the outer faces of the membrane, is portrayed within a system plus reservoir strategy. Induced by the interaction, renormalizations of the membrane capacitance and of a membrane voltage dependent potential are found to arise. Consequently, the equations of motion, for the expectation values of the variables and the pair correlation functions, are obtained in the collective membrane voltage space.

Influence of external magnetic field on dynamics of open quantum systems

The influence of an external magnetic field on the non-Markovian dynamics of an open two-dimensional quantum system is investigated. The fluctuations of collective coordinate and momentum and transport coefficients are studied for a charged harmonic oscillator linearly coupled to a neutral bosonic heat bath. It is shown that the dissipation of collective energy slows down with increasing strength of the external magnetic field. The role of magnetic field in the diffusion processes is illustrated by several examples.

Quantum master equations from classical Lagrangians with two stochastic forces

We show how a large family of master equations, describing quantum Brownian motion of a harmonic oscillator with translationally invariant damping, can be derived within a phenomenological approach, based on the assumption that an environment can be simulated by two classical stochastic forces. This family is determined by three time-dependent correlation functions (besides the frequency and damping coefficients), and it includes as special cases the known master equations, whose dissipative part is bilinear with respect to the operators of coordinate and momentum.

Transport coefficients of a quantum system interacting with a squeezed heat bath

The analytical expressions for the time-dependent friction and diffusion coefficients are presented for the case of coupling in coordinates between the collective subsystem and a squeezed heat bath. The effects of initial phase-sensitive and -insensitive correlations of the heat bath on the diffusion coefficients, fluctuations, and decoherence are studied. The interplay between friction and decoherence is discussed.

Studying open quantum systems by means of a deterministic approach to approximate functional integration

Representation of propagator for open quantum systems in the form of a double functional integral with respect to conditional Wiener measure is proposed. It allows one to apply the approximate formulas exact for functional polynomials of a certain power to calculation of such integrals. Within this deterministic approach the problem is reduced to evaluation of usual (Riemann) integrals of low multiplicity. The formulas are in fact the basis of a numerical method of studying time evolution of the systems. The features of the method are discussed and some examples of calculations are given.

Non-Markovian dynamics of quantum systems. II. Decay rate, capture, and pure states

On the basis of a master equation for the reduced density matrix of open quantum systems, we study the influence of time-dependent friction and diffusion coefficients on the decay rate from a potential well and the capture probability into a potential well. Taking into account the mixed diffusion coefficient Dqp, the quasistationary decay rates are compared with the analytically derived Kramers-type formulas for different temperatures and frictions. The diffusion coefficients supplying the purity of states are derived for a non-Markovian dynamics.