We shall revisit the conventional treatment of open quantum devices based on the Wigner-Function formalism. Our analysis will show that the artificial spatial separation between device active region and external reservoirs -properly defined within a semiclassical simulation scheme- is intrinsically incompatible with the non-local character of quantum mechanics. More specifically, by means of an exactly-solvable semiconductor model, we shall show that the application of the conventional boundary-condition scheme to the Wigner transport equation may produce highly non-physical results, like thermal injection of coherent state superpositions and boundary-driven negative probability distributions.
We shall revisit the conventional treatment of open quantum devices based on the Wigner-Function formalism. Our analysis will show that the artificial spatial separation between device active region and external reservoirs -properly defined within a semiclassical simulation scheme- is intrinsically incompatible with the non-local character of quantum mechanics. More specifically, by means of an exactly-solvable semiconductor model, we shall show that the application of the conventional boundary-condition scheme to the Wigner transport equation may produce highly non-physical results, like thermal injection of coherent state superpositions and boundary-driven negative probability distributions.
Quantum non‐locality is here put at variance with spatial contacts, as modelled within the Wigner‐Function formalism: we shall show how these two concepts are indeed intrinsically incompatible when applied to transport through quantum devices. More specifically, by means of an exactly‐solvable semiconductor model, we show that the application of the usual Up‐Wind boundary scheme to the Wigner transport equation may produce highly non‐physical results, like boundary‐driven negative probability distributions.
ABSTRACT: The concept of open quantum system is very broad and it is related to the ability of measuring only certain degree of freedoms of a particular system. Although this idea is relatively simple, the separation between the system of interest, the degree of freedoms that are accesible experimentally, and the reservoir, the degree of freedoms that are not accesible experimentally, is not always clear. For instance, in molecular systems, electronic spectroscopy has access only to electronic degree of freedoms so that the nuclear and vibrational degree of freedom become the reservoir, this makes its description not trivial. This scenario leads to have non-trivial and structured reservoirs and to develop powerful tools to analyze them. The hallmark of non-trivial and structured reservoirs is the non-Markovian dynamics. By translating the Feynman and Vernon influence functional approach into phase-space representation, we develop two theories of semiclassical evolution of the Wigner function of the system of interest that incorporate non-Markovian dynamics and highly non-trivial quantum effects such as non-locality of quantum mechanics: (i) We translate the Caldeira-Leggett model into phase-space representation of quantum mechanics and (ii) we consider the possibility of having non-linear baths and therefore, truly quantum reservoirs. During the last forty years the study of energy loss and coherence in quantum systems has been based on the Ullersma-Caldeira-Leggett model, a model that describes the environment of quantum systems of interest as a collection of harmonic oscillators with classical evolution. We constructed this model in the Wigner-Weyl representation of quantum mechanics and discuss the classical nature of the evolution of the bath modes and the semiclassical evolution of the central system. As an application of the semiclassical Wigner propagator, the non-Markovian time evolution under the Morse potencial is analyzed. There, it is clear how decohering processes shrink the propagator to smaller regions of phase space implying that the dynamics become more local, i.e., more classical. The current level of experimentation and control of physical systems have called into question the validity of the model in, one hand, molecular systems (e.g. photosynthetic complexes immersed in solvents, chemical systems in liquid phase or gas and manipulated with intense laser pulses) and, in the other hand, solid state systems (e.g. Josephson junctions, spins in quantum dots or "spinning ice"). Given the importance of these systems in the development of new quantum technologies and in the understanding of quantum phenomena in mesoscopic systems, it has become necessary to develop new models of the environment and efficient methodologies with quantitative prediction power. However, some of them are artificial modifications of the Ullersma-Caldeira-Leggett model without solid and clean physical support. Here we formulated a general framework that allows the study of quantum correlations in quantum systems in the presence of non-harmonic thermal baths (e.g. baths formed by strongly coupled diatomic molecules). This formulation will allow a more precise and quantitative description of processes such as the transport of excitons in photosynthetic complexes, the transfer of heat in solid state devices, among others. Results clearly show the non-classical time dynamics of the bath modes. The implementation of this particular theory remains, however, as a challenge.
A general density-matrix description of energy-dissipation and decoherence phenomena in open quantum systems is presented. More specifically, contrary to the conventional single-particle correlation expansion, we shall investigate the effect of the adiabatic or Markov limit, before considering/performing any reduction procedure. Our fully operatorial approach allows us to better identify the general properties of the scattering superoperators entering our effective quantum-transport theory at various description levels. In particular, we shall show that—contrary to the semiclassical case—the conventional Markov limit does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this serious limitation, originally pointed out and partially solved by Davies and co-workers almost three decades ago, we shall propose an alternative and more general adiabatic procedure, which (i) in the semiclassical limit reduces to the standard Fermi's golden rule, and (ii) describes a genuine Lindblad evolution, thus providing a reliable/robust treatment of energy-dissipation and dephasing processes in semiconductor quantum devices
Quantum information and quantum communication are both strongly based on concepts of quantum superposition and entanglement. Entanglement allows distinct bodies, that share a common origin or that have interacted in the past, to continue to be described by the same wave function until evolution is coherent. So, there is an equivalence between coherence and entanglement. In this paper, we show the relation between quantum coherence and quantum interference and the negative parts of the Wigner quasi-distribution, using the Wigner signed-particle formulation. A simple physical problem consisting of electrons in a nanowire interacting with the potential of a repulsive dopant placed in the center of it creates a quasi two-slit electron system that separates the wave function into two entangled branches. The analysis of the Wigner quasi-distribution of this problem establishes that its negative part is principally concentrated in the region after the dopant between the two entangled branches, maintaining the coherence between them. Moreover, quantum interference is shown in this region both in the positive and in the negative part of the Wigner function and is produced by the superposition of Wigner functions evaluated at points of the momentum space that are symmetric with respect to the initial momentum of the injected electrons.
Correct use of the Wigner representation of quantum mechanics, which is realized with joint distributions of quasiprobabilities in phase space, requires the use of certain specific rules and attention to a number of properties which distinguish the quasiprobability from a true probability. This paper is mainly concerned with these problems. In the Wigner representation the quantum Liouville equation appears instead of the Schroedinger equation. The solution may have no physical meaning unless it is subjected to a necessary and sufficient condition which selects an allowed class of distributions which describe quantum-mechanical pure states. This condition contains Planck's constant and imposes, besides the uncertainty relations, severe restrictions on the possible form of the Wigner function. When this condition is satisfied, one can reconstruct the wave function from the Wigner function. In the case of an oscillator, the quantization condition for the energies of the stationary states does not follow from the Liouville equation, but from this supplementary condition. Unlike the true probability density, any Wigner function (except Gaussian ones) of a pure state takes on negative values. Another important peculiarity is that the quasiprobability is not concentrated on certain hypersurfaces, but is smeared out over the entire phase space. These and other features considered in this paper should be kept in mind when using the Wigner representation in quantum-mechanical problems.