Special Issue "Quantum Dynamics with Non-Hermitian Hamiltonians"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: 31 August 2020.

Special Issue Editor

Prof. Dr. Alessandro Sergi
Website
Guest Editor
Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
Interests: non-Hermitian quantum mechanics; quantum-classical hybrid systems; non-Hamiltonian systems; open quantum systems; superfluid vacuum theory; action-at-a-distance classical and quantum theories; emergent quantum gravity; dark energy; analogue gravity phenomenology
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Special Issue Information

Dear Colleagues,

Non-Hermitian quantum dynamics is a topic in theoretical physics that, in recent years, has enjoyed a thriving time of exceptional development. Since its first steps, from being found in Landau’s comments about wave functions scattering to infinity and in Gamow’s description of quantum tunneling, this area of research has reached an advanced state of formalization where its applications range from chemical and condensed matter systems to optics, quantum field theory, and cosmology. Non-Hermitian quantum dynamics addresses open quantum systems from a unique and advantageous perspective; hence, it is as ubiquitous as open quantum systems are. Despite its successes, many questions fundamental in nature remain open for investigation, and the list of its possible applications continues to grow. The target of this Special Issue is to show the great effectiveness of non-Hermitian formulations of quantum dynamics as a tool to investigate, for example, resonances, topological systems, quantum transport, exceptional points, nuclear phenomena, optics and photonics, relativistic quantum processes, quantum fields, and cosmology, to name a few. Papers dealing with the above topics, and non-Hermitian quantum dynamics in general, are welcome to this Special Issue whose broad scope is to reflect both the quick development of the field and its potential for further growth.

Prof. Dr. Alessandro Sergi
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

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Keywords

  • non-Hermitian quantum dynamics
  • non-Hermitian Hamiltonians
  • non-Hermitian quantum field theory
  • open quantum systems
  • resonances
  • topological systems
  • relativistic dynamics
  • cosmology

Published Papers (4 papers)

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Research

Open AccessArticle
Time-Dependent Pseudo-Hermitian Hamiltonians and a Hidden Geometric Aspect of Quantum Mechanics
Entropy 2020, 22(4), 471; https://doi.org/10.3390/e22040471 - 20 Apr 2020
Abstract
A non-Hermitian operator H defined in a Hilbert space with inner product ·|· may serve as the Hamiltonian for a unitary quantum system if it is η-pseudo-Hermitian for a metric operator (positive-definite automorphism) η. The latter defines [...] Read more.
A non-Hermitian operator H defined in a Hilbert space with inner product · | · may serve as the Hamiltonian for a unitary quantum system if it is η -pseudo-Hermitian for a metric operator (positive-definite automorphism) η . The latter defines the inner product · | η · of the physical Hilbert space H η of the system. For situations where some of the eigenstates of H depend on time, η becomes time-dependent. Therefore, the system has a non-stationary Hilbert space. Such quantum systems, which are also encountered in the study of quantum mechanics in cosmological backgrounds, suffer from a conflict between the unitarity of time evolution and the unobservability of the Hamiltonian. Their proper treatment requires a geometric framework which clarifies the notion of the energy observable and leads to a geometric extension of quantum mechanics (GEQM). We provide a general introduction to the subject, review some of the recent developments, offer a straightforward description of the Heisenberg-picture formulation of the dynamics for quantum systems having a time-dependent Hilbert space, and outline the Heisenberg-picture formulation of dynamics in GEQM. Full article
(This article belongs to the Special Issue Quantum Dynamics with Non-Hermitian Hamiltonians)
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Open AccessArticle
Non-Hermitian Hamiltonians and Quantum Transport in Multi-Terminal Conductors
Entropy 2020, 22(4), 459; https://doi.org/10.3390/e22040459 - 17 Apr 2020
Abstract
We study the transport properties of multi-terminal Hermitian structures within the non-equilibrium Green’s function formalism in a tight-binding approximation. We show that non-Hermitian Hamiltonians naturally appear in the description of coherent tunneling and are indispensable for the derivation of a general compact expression [...] Read more.
We study the transport properties of multi-terminal Hermitian structures within the non-equilibrium Green’s function formalism in a tight-binding approximation. We show that non-Hermitian Hamiltonians naturally appear in the description of coherent tunneling and are indispensable for the derivation of a general compact expression for the lead-to-lead transmission coefficients of an arbitrary multi-terminal system. This expression can be easily analyzed, and a robust set of conditions for finding zero and unity transmissions (even in the presence of extra electrodes) can be formulated. Using the proposed formalism, a detailed comparison between three- and two-terminal systems is performed, and it is shown, in particular, that transmission at bound states in the continuum does not change with the third electrode insertion. The main conclusions are illustratively exemplified by some three-terminal toy models. For instance, the influence of the tunneling coupling to the gate electrode is discussed for a model of quantum interference transistor. The results of this paper will be of high interest, in particular, within the field of quantum design of molecular electronic devices. Full article
(This article belongs to the Special Issue Quantum Dynamics with Non-Hermitian Hamiltonians)
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Open AccessArticle
Control of the Geometric Phase in Two Open Qubit–Cavity Systems Linked by a Waveguide
Entropy 2020, 22(1), 85; https://doi.org/10.3390/e22010085 - 10 Jan 2020
Abstract
We explore the geometric phase in a system of two non-interacting qubits embedded in two separated open cavities linked via an optical fiber and leaking photons to the external environment. The dynamical behavior of the generated geometric phase is investigated under the physical [...] Read more.
We explore the geometric phase in a system of two non-interacting qubits embedded in two separated open cavities linked via an optical fiber and leaking photons to the external environment. The dynamical behavior of the generated geometric phase is investigated under the physical parameter effects of the coupling constants of both the qubit–cavity and the fiber–cavity interactions, the resonance/off-resonance qubit–field interactions, and the cavity dissipations. It is found that these the physical parameters lead to generating, disappearing and controlling the number and the shape (instantaneous/rectangular) of the geometric phase oscillations. Full article
(This article belongs to the Special Issue Quantum Dynamics with Non-Hermitian Hamiltonians)
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Open AccessArticle
Theory of Response to Perturbations in Non-Hermitian Systems Using Five-Hilbert-Space Reformulation of Unitary Quantum Mechanics
Entropy 2020, 22(1), 80; https://doi.org/10.3390/e22010080 - 09 Jan 2020
Abstract
Non-Hermitian quantum-Hamiltonian-candidate combination Hλ of a non-Hermitian unperturbed operator H=H0 with an arbitrary “small” non-Hermitian perturbation λW is given a mathematically consistent unitary-evolution interpretation. The formalism generalizes the conventional constructive Rayleigh–Schrödinger perturbation expansion technique. It is sufficiently general [...] Read more.
Non-Hermitian quantum-Hamiltonian-candidate combination H λ of a non-Hermitian unperturbed operator H = H 0 with an arbitrary “small” non-Hermitian perturbation λ W is given a mathematically consistent unitary-evolution interpretation. The formalism generalizes the conventional constructive Rayleigh–Schrödinger perturbation expansion technique. It is sufficiently general to take into account the well known formal ambiguity of reconstruction of the correct physical Hilbert space of states. The possibility of removal of the ambiguity via a complete, irreducible set of observables is also discussed. Full article
(This article belongs to the Special Issue Quantum Dynamics with Non-Hermitian Hamiltonians)

Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

1. Ali Mostafazadeh

2. Antonino Messina

3. Alessandro Sergi

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