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Entropy
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Quantum Dynamics with Non-hermitian Hamiltonians II
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Quantum Dynamics with Non-hermitian Hamiltonians II

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

Deadline for manuscript submissions: 17 June 2024 | Viewed by 4352

Special Issue Editors

Prof. Alessandro Sergi

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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-adiabatic dynamics; non-Hamiltonian systems; open quantum systems
Special Issues, Collections and Topics in MDPI journals
Prof. Antonino Messina

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Guest Editor
Department of Mathematics and Computer Science, University of Palermo, 90133 Palermo, PA, Italy
Interests: quantum electrodynamics; open systems; time dependent spin Hamiltonians; quantum and semiclassical Rabi models
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nowadays, non-Hermitian quantum dynamics is a well-established and continuously growing field of research. Either PT-symmetric or non-PT-symmetric Hamiltonians are usually considered. The symmetric ones represent non-equilibrium systems in a steady state, while the non-PT-symmetric describe systems in more general non-equilibrium states. Because of this, the formulation of the quantum statistical mechanics of general non-Hermitian quantum systems is at least as difficult as the theory of general non-equilibrium statistical systems. Nevertheless, the theoretical applications of non-Hermitian Hamiltonians are found in the fields of condensed matter, optics, and photonics; non-Hermitian Hamiltonians are also used to study exceptional points, resonances, nuclear phenomena, relativistic quantum processes, topological systems, and quantum transport. Let us also not forget that quantum field theory and cosmology are a playground for non-Hermitian mathematical approaches.

However, so far, experimental developments in this field have not been on par with theoretical achievements. Until now, the observation of genuine non-Hermitian dynamics in experiments has only concerned the evolution of classical dissipative systems, theoretically mapped onto quantum-like non-Hermitian dynamics. This can be achieved in a relatively easy manner by means of asymmetric attenuation and amplification. True non-Hermitian evolution of quantum systems is inherently a hard problem since quantum systems naturally follow Hermitian dynamics. Promising ways to achieve a genuine non-Hermitian evolution of quantum systems are given by coupling quantum systems to ancillae and the approach of dilation.

The scope of this Special Issue is broad. The goal is to gather contributions dealing with all the above topics and open problems. The hope is to present the state of the art in non-Hermitian dynamics and to identify the stepping stones for further progress.

Prof. Alessandro Sergi
Prof. Antonino Messina
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Related Special Issue

Published Papers (4 papers)

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Research

23 pages, 381 KiB  
Article
Consistent Treatment of Quantum Systems with a Time-Dependent Hilbert Space
by Ali Mostafazadeh
Entropy 2024, 26(4), 314; https://doi.org/10.3390/e26040314 - 03 Apr 2024
Viewed by 430
Abstract
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a time-independent Hilbert space. We show that in general [...] Read more.
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a time-independent Hilbert space. We show that in general the Hamiltonian operator does not represent an observable of the system even if it is a self-adjoint operator. This is related to a hidden geometric aspect of quantum mechanics arising from the presence of an operator-valued gauge potential. We also offer a careful treatment of quantum systems whose Hilbert space is obtained by endowing a time-independent vector space with a time-dependent inner product. Full article
(This article belongs to the Special Issue Quantum Dynamics with Non-hermitian Hamiltonians II)
11 pages, 549 KiB  
Article
Parity-Time Symmetric Holographic Principle
by Xingrui Song and Kater Murch
Entropy 2023, 25(11), 1523; https://doi.org/10.3390/e25111523 - 07 Nov 2023
Viewed by 1006
Abstract
Originating from the Hamiltonian of a single qubit system, the phenomenon of the avoided level crossing is ubiquitous in multiple branches of physics, including the Landau–Zener transition in atomic, molecular, and optical physics, the band structure of condensed matter physics and the dispersion [...] Read more.
Originating from the Hamiltonian of a single qubit system, the phenomenon of the avoided level crossing is ubiquitous in multiple branches of physics, including the Landau–Zener transition in atomic, molecular, and optical physics, the band structure of condensed matter physics and the dispersion relation of relativistic quantum physics. We revisit this fundamental phenomenon in the simple example of a spinless relativistic quantum particle traveling in (1+1)-dimensional space-time and establish its relation to a spin-1/2 system evolving under a PT-symmetric Hamiltonian. This relation allows us to simulate 1-dimensional eigenvalue problems with a single qubit. Generalizing this relation to the eigenenergy problem of a bulk system with N spatial dimensions reveals that its eigenvalue problem can be mapped onto the time evolution of the edge state with (N−1) spatial dimensions governed by a non-Hermitian Hamiltonian. In other words, the bulk eigenenergy state is encoded in the edge state as a hologram, which can be decoded by the propagation of the edge state in the temporal dimension. We argue that the evolution will be PT-symmetric as long as the bulk system admits parity symmetry. Our work finds the application of PT-symmetric and non-Hermitian physics in quantum simulation and provides insights into the fundamental symmetries. Full article
(This article belongs to the Special Issue Quantum Dynamics with Non-hermitian Hamiltonians II)
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9 pages, 291 KiB  
Article
Analogue Hawking Radiation as a Tunneling in a Two-Level PT-Symmetric System
by Bijan Bagchi, Rahul Ghosh and Sauvik Sen
Entropy 2023, 25(8), 1202; https://doi.org/10.3390/e25081202 - 12 Aug 2023
Cited by 1 | Viewed by 1022
Abstract
In light of a general scenario of a two-level non-Hermitian PT-symmetric Hamiltonian, we apply the tetrad-based method to analyze the possibility of analogue Hawking radiation. We carry this out by making use of the conventional null-geodesic approach, wherein the associated Hawking radiation [...] Read more.
In light of a general scenario of a two-level non-Hermitian PT-symmetric Hamiltonian, we apply the tetrad-based method to analyze the possibility of analogue Hawking radiation. We carry this out by making use of the conventional null-geodesic approach, wherein the associated Hawking radiation is described as a quantum tunneling process across a classically forbidden barrier on which the event horizon imposes. An interesting aspect of our result is that our estimate for the tunneling probability is independent of the non-Hermitian parameter that defines the guiding Hamiltonian. Full article
(This article belongs to the Special Issue Quantum Dynamics with Non-hermitian Hamiltonians II)
16 pages, 335 KiB  
Article
Non-Stationary Non-Hermitian “Wrong-Sign” Quantum Oscillators and Their Meaningful Physical Interpretation
by Miloslav Znojil
Entropy 2023, 25(4), 692; https://doi.org/10.3390/e25040692 - 19 Apr 2023
Cited by 3 | Viewed by 983
Abstract
In the framework of quantum mechanics using quasi-Hermitian operators the standard unitary evolution of a non-stationary but still closed quantum system is only properly described in the non-Hermitian interaction picture (NIP). In this formulation of the theory both the states and the observables [...] Read more.
In the framework of quantum mechanics using quasi-Hermitian operators the standard unitary evolution of a non-stationary but still closed quantum system is only properly described in the non-Hermitian interaction picture (NIP). In this formulation of the theory both the states and the observables vary with time. A few aspects of implementation of this picture are illustrated via the “wrong-sign” quartic oscillators. It is shown that in contrast to the widespread belief, both of the related Schrödinger-equation generators G(t) and the Heisenberg-equation generators Σ(t) are just auxiliary concepts. Their spectra are phenomenologically irrelevant and, in general, complex. It is argued that only the sum H(t)=G(t)+Σ(t) of the latter operators retains the standard physical meaning of the instantaneous energy of the unitary quantum system in question. Full article
(This article belongs to the Special Issue Quantum Dynamics with Non-hermitian Hamiltonians II)
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