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Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physics

Quantum non‐locality in systems with open boundaries: From the Wigner‐function formalism to non‐homogeneous Markovian master equations

David Taj, Fausto Rossi

Published Oct 12, 2007• 1 citation
Publisher

Abstract

Abstract We shall discuss the role of electrical contacts within the conventional treatment of quantum devices based on the Wigner‐Function formalism. Our analysis will show that the artificial spatial separation between device active region and external reservoirs, being intrinsically incompatible with the non‐local character of quantum mechanics, may produce highly non‐physical results like boundary‐driven negative probability distributions. To overcome this serious limitation, we shall propose a new strategy to properly separate device and reservoir degrees of freedom, based on the well known projection techniques used in the formal theory of open systems. Our main result is a non‐Markovian master equation, where dissipation and dephasing phenomena are also induced by the presence of spatially external particle reservoirs. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssc.200776527

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Abstract We shall discuss the role of electrical contacts within the conventional treatment of quantum devices based on the Wigner‐Function formalism. Our analysis will show that the artificial spatial separation between device active region and external reservoirs, being intrinsically incompatible with the non‐local character of quantum mechanics, may produce highly non‐physical results like boundary‐driven negative probability distributions. To overcome this serious limitation, we shall propose a new strategy to properly separate device and reservoir degrees of freedom, based on the well known projection techniques used in the formal theory of open systems. Our main result is a non‐Markovian master equation, where dissipation and dephasing phenomena are also induced by the presence of spatially external particle reservoirs. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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 We review our recent contributions to two topics that have become of interest in the field of open, dissipative quantum systems: non‐Gaussian noise and decoherence in fermionic systems. Decoherence by non‐Gaussian noise, i.e. by an environment that cannot be approximated as a bath of harmonic oscillators, is important in nanostructures (e.g. qubits) where there might be strong coupling to a small number of fluctuators. We first revisit the pedagogical example of dephasing by classical telegraph noise. Then we address two models where the quantum nature of the noise becomes essential: “quantum telegraph noise” and dephasing by electronic shot noise. In fermionic systems, many‐body aspects and the Pauli principle have to be taken care of when describing the loss of phase coherence. This is relevant in electronic quantum transport through metallic and semiconducting structures. Specifically, we recount our recent results regarding dephasing in a chiral interacting electron liquid, as it is realized in the electronic Mach–Zehnder interferometer. This model can be solved employing the technique of bosonization as well as a physically transparent semiclassical method (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Abstract We shall revisit the conventional adiabatic or Markov approximation, stressing its intrinsic failure in describing the proper quantum‐mechanical evolution of a generic subsystem interacting with its environment. In particular, we shall show that – contrary to the semiclassical case – the Markov limit does not preserve the positivedefinite character of the corresponding density matrix, thus leading to highly non‐physical results. To overcome this problem, we shall propose an alternative adiabatic procedure which (i) in the semiclassical limit reduces to the standard Fermi's golden rule, and (ii) describes a genuine Limblad evolution, thus providing a reliable/robust treatment of energy‐dissipation and dephasing processes in electronic quantum devices. Compared to standard master‐equation formulations, the proposed approach does not involve/require any reduction or average procedure, exactly as for the derivation of the well known Fermi's golden rule. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Open quantum systems are often encountered in many different physical situations. From quantum optics to statistical mechanics, they are fundamental in the understanding of a great variety of different phenomena. Some of the most common examples are the relaxation to equilibrium, the existence of nonequilibrium stationary states, and the dynamics of atoms in interaction with electromagnetic fields. A crucial step in the analysis is to consider the quantum open system and its environment as the two mutually interacting components of a larger isolated system. Thereafter, the so‐called Markov approximation is often considered, which consists on assuming that the time scales associated to the dynamics of the quantum open system are larger than those of the environment. It is the interplay of the different time scales associated with the system and the environment what determines the validity of the different approximations made. In this paper we will discuss the dynamics of a open quantum system in contact with a reservoir when the Markov approximation is not valid, and we have to include some non‐Markovian or memory effects.
Quantum mechanics must be regarded as open systems. On one hand, this is due to the fact that, like in classical physics, any realistic system is subjected to a coupling to an uncontrollable environment which influences it in a non-negligible way. The theory of open quantum systems thus plays a major role in many applications of quantum physics since perfect isolation of quantum system is not possible and since a complete microscopic description or control of the environment degrees of freedom is not feasible or only partially so [1]. Practical considerations therefore force one to seek for a simpler, effectively probabilistic description in terms of an open system. There is a close physical and mathematical connection between the evolution of an open system, the state changes induced by quantum measurements, and the classical notion of a stochastic process. The paper provides a bibliographic review of this interrelations, it shows the mathematical equivalence between markovian master equation and generalized piecewise deterministic processes [1] and it introduces the open system in an open observed environment model.