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We show that the pointer basis distinguished by collisional decoherence consists of exponentially localized, solitonic wave packets. Based on the orthogonal unraveling of the quantum master equation, we characterize their formation and dynamics, and we demonstrate that the statistical weights arising from an initial superposition state are given by the required projection. Since the spatial width of the pointer states can be obtained by accounting for the gas environment in a microscopically realistic fashion, one may thus calculate the coherence length of a strongly interacting gas., Comment: 8 pages, 1 figure; corresponds to published version

Two noninteracting atoms, initially entangled in Bell states, are coupled to a one-mode cavity. Based on the reduced non-perturbative quantum master equation, the entanglement evolution of the two atoms with decay is investigated beyond rotating-wave approximation. It is shown that the counter-rotating wave terms have great influence on the disentanglement behavior. The phenomenon of entanglement sudden death and entanglement sudden birth will occur.

Exact quantum master equation for a driven Brownian oscillator system is constructed via a Wigner phase-space Gaussian wave packet approach. The interplay between external field and dissipation leads to this system an effective field correction that enhances the polarization. This cooperative property is resulted from an effective bath response to the external field applied on the system. It is important in the low-frequency driving and intermediate bath memory region. We demonstrate this non-Markovian effect on the linear response and nonlinear dynamics and analyze the results together with analytical asymptotic expressions., Comment: 8 pages, 7 figures, submitted to J. Chem. Phys

We study the structure of the time evolution of the density matrix in contact with a thermal bath in a standard projection operator sheme. The reduced density matrix of the system in the steady state is obtained by tracing out the degree of freedom of the thermal bath from the equilibrium density matrix of the total system. This reduced density matrix is modified by the interaction, and is different from that of the equilibrium of the system alone. We explicitly calculate the contribution of each term in quantum master equation to the realization of the steady state density matrix, and make clear roles of each term. By making use of the role of each term, the properties of the commonly used quantum master equation are examined., 17 pages, to appear in JPSJ

We show that, in the weak coupling limit, the laser model process converges weakly in the sense of the matrix elements to a quantum diffusion whose equation is explicitly obtained. We prove convergence, in the same sense, of the Heisenberg evolution of an observable of the system to the solution of a quantum Langevin equation. As a corollary of this result, via the quantum Feynman-Kac technique, one can recover previous results on the quantum master equation for reduced evolutions of open systems. When applied to some particular model (e.g. the free Boson gas) our results allow to interpret the Lamb shift as an Ito correction term and to express the pumping rates in terms of quantities related to the original Hamiltonian model.

The quantum Brownian motion of a particle in a periodic potential V(x)=−V0cos(x/x0) is treated using the master equation for the Wigner distribution function W(x, p, t) in phase space (x, p). Explicit equations for the diffusion coefficients of the master equation for this dissipative quantum system are derived. The dynamic structure factor S(k, t) and escape rate Γ are evaluated using matrix continued fractions. The matrix continued fraction calculation for Γ agrees well with the analytical solution of the corresponding quantum Kramers turnover problem.

The purpose of this paper is to study the optimal performance for an irreversible quantum Brayton engine consisting of two constant-frequency branches connected by two irreversible adiabatic branches. The solution of the generalized quantum master equation of a thermal system is obtained in the Heisenberg picture. The optimization region (or criteria) for an irreversible quantum Brayton engine is obtained. The relationship between the dimensionless power output P* versus efficiency η for the irreversible quantum Brayton engine with heat leakage and other irreversible losses are derived.

The calculation of chemical reaction rates in the condensed phase is a central preoccupation of theoretical chemistry. At low temperatures, quantum-mechanical effects can be significant and even dominant; yet quantum calculations of rate constants are extremely challenging, requiring theories and methods capable of describing quantum evolution in the presence of dissipation. In this paper we present a new approach based on the use of a non-Markovian quantum master equation (NM-QME). As opposed to other approximate quantum methods, the quantum dynamics of the system coordinate is treated exactly; hence there is no loss of accuracy at low temperatures. However, because of the perturbative nature of the NM-QME it breaks down for dimensionless frictions larger than about 0.1. We show that by augmenting the system coordinate with a collective mode of the bath, the regime of validity of the non-Markovian master equation can be extended significantly, up to dimensionless frictions of 0.5 over the entire temperature range. In the energy representation, the scaling goes as the number of levels in the relevant energy range to the third power. This scaling is not prohibitive even for chemical systems with many levels; hence we believe that the current method will find a useful place alongside the existing techniques for calculating quantum condensed-phase rate constants.

For the description of dynamical effects in quantum mechanical systems on ultrashort time scales, memory effects play an important role. Meier and Tannor [J. Chem. Phys. 111, 3365 (1999)] developed an approach which is based on a time-nonlocal scheme employing a numerical decomposition of the spectral density. Here we propose two different approaches which are based on a partial time-ordering prescription, i.e., a time-local formalism and also on a numerical decomposition of the spectral density. In special cases such as the Debye spectral density the present scheme can be employed even without the numerical decomposition of the spectral density. One of the proposed schemes is valid for time-independent Hamiltonians and can be given in a compact quantum master equation. In the case of time-dependent Hamiltonians one has to introduce auxiliary operators which have to be propagated in time along with the density matrix. For the example of a damped harmonic oscillator these non-Markovian theories are compared among each other, to the Markovian limit neglecting memory effects and time dependencies, and to exact path integral calculations. Good agreement between the exact calculations and the non-Markovian results is obtained. Some of the non-Markovian theories mentioned above treat the time dependence in the system Hamiltonians nonperturbatively. Therefore these methods can be used for the simulation of experiments with arbitrary large laser fields.

Using the Pauli-Villars regularization, we make a perturbative analysis of the quantum master equation (QME), Σ = 0, for the Wilsonian effective action. It is found that the QME for the UV action determines whether exact gauge symmetry is realized along the renormalization group (RG) flow. The basic task of solving the QME can be reduced to compute the Troost-van Niuwenhuizen-Van Proeyen jacobian factor for the classical UV action. When the QME cannot be satisfied, the non-vanishing Σ is proportional to a BRS anomaly, which is shown to be preserved along the RG flow. To see how the UV action fulfills the QME in anomaly free theory, we calculate the jacobian factor for a pure Yang-Mills theory in four dimensions.

We study a dynamical scheme for condensation of bosonic trapped gases beyond the Lamb-Dicke limit, when the photon-recoil energy is larger than the energy spacing of the trap. Using quantum master equation formalism we demonstrate that dark-state cooling methods similar to those designed for a single trapped atom allow for the condensation of a collection of bosons into a single state of the trap, either the ground, or an excited state. By means of Monte-Carlo simulations we analyse the condensation dynamics for different dimensions, and for different cooling schemes.

We show that the general quantum master equation used in quantum optics can be put in the form of Lindblad’s master equation obtained in the frame of the general theory of the dynamical semigroups. In this case, the dissipative interaction is described in the most general form by a system of openness parameters. We find the expressions of these parameters as functions of the operators of the dissipative environment.

Solving the Pauli quantum master equation by means of a method proposed by van Kampen and recently developed by Tomita and Tomita, we give a quantitative description of the evolution to wards the equilibrium state of a quantum macrosystem and of the fluctuations around the mean values of its energy. The probability distribution of these fluctuations turns out to be of a Gaussian shape with a variance function of time and approaching, fort→∞, a constant value. Finally an application is made to the phenomenon of spin relaxation.

The nature of the noise described by the c -number quantum Langevin equation is investigated. Subtleties in the stochastic calculus are shown to originate from differences between noise and classical coloured noise. The Fokker- Planck equation for the Wigner distribution and the associated quantum master equation are derived for a linear system. Explicit results for the quasiprobabilities are obtained.

Considering a simple quantum master equation for a free particle we prove that after a given period of relaxation the solutions can be interpreted exactly in terms of uniform localized wave packets whose centers imitate classical trajectories.

An exact generalized master equation is derived for a large quantum-mechanical system in the form of a power series in the density. This derivation is a quantum-mechanical generalization of a previous work by the author for classical systems. The quantum equation can be viewed as a time-dependent analog of the virial expansion of the quantum-mechanical partition function\char22{}for both degenerate systems (Bose-Einstein or Fermi-Dirac statistics) and nondegenerate systems. The coefficients of the series, in the quantum master equation, are explicitly given in terms of operators (Green functions) which are determined by the dynamics of isolated groups of particles and are convergent functions of the interaction potential. Equations are obtained for the off-diagonal elements of the density matrix as well as for the diagonal elements. The equation for the diagonal elements is shown to reduce to a Markoffian master equation for asymptotically long times, and an explicit expression is obtained for the "scattering" operator of this asymptotic equation.

In the framework of a general theory of open quantum systems, we obtain a quantum master equation for the two-level atom interacting with a single mode of the electromagnetic field. On this basis, we obtain new optical equations. In comparison with the conventional Bloch-Feynman optical equations which contain three phenomenological parameters, the new equations contain nine phenomenological parameters. New physical effects , due to the opening of the system, are predicted: 1) a resonance frequency shift, 2) an asymmetry of the spectral line, 3) a modification of the dependence of the absorbtion coefficient and of the nonlinear dephasing on the atomic detuning, and 4) an additional nonlinear dependence of the absorbtion coefficient on the electric field. For a rather small atom density when the fourth effect can be neglected,we found an analytical expression of the transmittivity characteristic of an optical bistable Fabry-Perot resonator and found a good agreement with the experiment.

The coherent time evolution of electrons in double quantum dots induced by fast bias-voltage switches is studied theoretically. As it was shown experimentally, such driven double quantum dots are potential devices for controlled manipulation of charge qubits. By numerically solving a quantum master equation we obtain the energy- and time-resolved electron transfer through the device which resembles the measured data. The observed oscillations are found to depend on the level offset of the two dots during the manipulation and, most surprisingly, also the on initialization stage. By means of an analytical expression, obtained from a large-bias model, we can understand the prominent features of these oscillations seen in both the experimental data and the numerical results. These findings strengthen the common interpretation in terms of a coherent transfer of electrons between the dots.

Stochastic exclusion processes play an integral role in the physics of non-equilibrium statistical mechanics. These models are Markovian processes, described by a classical master equation. In this paper a quantum mechanical version of a stochastic hopping process in one dimension is formulated in terms of a quantum master equation. This allows the investigation of coherent and stochastic evolution in the same formal framework. The focus lies on the non-equilibrium steady state. Two stochastic model systems are considered, the totally asymmetric exclusion process and the fully symmetric exclusion process. The steady state transport properties of these models is compared to the case with additional coherent evolution, generated by the $XX$-Hamiltonian.

We establish a theoretical method which goes beyond the weak coupling and Markovian approximations while remaining intuitive, using a quantum master equation in a larger Hilbert space. The method is applicable to all impurity Hamiltonians tunnel-coupled to one (or multiple) baths of free fermions. The accuracy of the method is in principle not limited by the system-bath coupling strength, but rather by the shape of the spectral density and it is especially suited to study situations far away from the wide-band limit. In analogy to the bosonic case, we call it the fermionic reaction coordinate mapping. As an application we consider a thermoelectric device made of two Coulomb-coupled quantum dots. We pay particular attention to the regime where this device operates as an autonomous Maxwell demon shoveling electrons against the voltage bias thanks to information. Contrary to previous studies we do not rely on a Markovian weak coupling description. Our numerical findings reveal that in the regime of strong coupling and non-Markovianity, the Maxwell demon is often doomed to disappear except in a narrow parameter regime of small power output., 18 pages incl. references, appendix and 10 figures; accepted version

We introduce a versatile method to compute electronic steady-state properties of strongly correlated extended quantum systems out of equilibrium. The approach is based on dynamical mean-field theory (DMFT), in which the original system is mapped onto an auxiliary nonequilibrium impurity problem imbedded in a Markovian environment. The steady-state Green's function of the auxiliary system is solved by full diagonalization of the corresponding Lindblad equation. The approach can be regarded as the nontrivial extension of the exact-diagonalization-based DMFT to the nonequilibrium case. As a first application, we consider an interacting Hubbard layer attached to two metallic leads and present results for the steady-state current and the nonequilibrium density of states.

The development of non-Hermitian topological band theory has led to observations of novel topological phenomena in effectively classical, driven, and dissipative systems. However, for open quantum many-body systems, the absence of a ground state presents a challenge to define robust signatures of non-Hermitian topology. We show that such a signature is provided by crossings in the time evolution of the entanglement spectrum. These crossings occur in quenches from the trivial to the topological phase of a driven-dissipative Kitaev chain that is described by a Markovian quantum master equation in Lindblad form. At the topological transition, which can be crossed either by changing parameters of the Hamiltonian of the system or by increasing the strength of dissipation, the timescale at which the first entanglement spectrum crossing occurs diverges with a dynamical critical exponent of $\ensuremath{\epsilon}=1/2$. We corroborate these numerical findings with an exact analytical solution of the quench dynamics for a spectrally flat postquench Liouvillian. This exact solution suggests an interpretation of the topological quench dynamics as a fermion parity pump. Our work thus reveals signatures of non-Hermitian topology that are unique to quantum many-body systems and cannot be emulated in classical simulators of non-Hermitian wave physics.

A dissipative bistable system presents the simplest model to describe condensed phase reaction dynamics. Using a quantum master equation approach to calculate multitime dipole correlation functions we demonstrate how the dissipative dynamics can be characterized by time-resolved third-order infrared spectroscopy. Thereby we incorporate bilinear and linear–quadratic system–bath interaction into the Redfield relaxation tensor. Investigating equilibrium and nonequilibrium initial conditions for a symmetric system it is shown that bath-induced coherence transfer can have a dramatic influence on the two-dimensional signals. This occurs when the inverse of the ground state tunneling splitting is of the order of the coherence transfer time.