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Related papers: The Non-Hermitian quantum mechanics and its canoni…

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We establish a unified framework for dynamical quantum phase transitions (DQPTs) in non-Hermitian systems that encompasses both biorthogonal and self-norm non-biorthogonal formulations for pure and mixed states under quantum quench…

Quantum Physics · Physics 2025-10-27 Yongxu Fu , Gao Xianlong

The introduction of nonlinearities in the Schr\"odinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear…

Quantum Physics · Physics 2024-03-08 David Navia , Ángel S. Sanz

The ordinary time-dependent perturbation theory of quantum mechanics, that describes the interaction of a stationary system with a time-dependent perturbation, predicts that the transition probabilities induced by the perturbation are…

Quantum Physics · Physics 2017-10-11 S. Longhi , G. Della Valle

Bohmian mechanics is the most naively obvious embedding imaginable of Schr\"odinger's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at…

Quantum Physics · Physics 2008-11-26 K. Berndl , M. Daumer , D. Dürr , S. Goldstein , N. Zanghi

The Stone theorem requires that in a physical Hilbert space ${\cal H}$ the time-evolution of a stable quantum system is unitary if and only if the corresponding Hamiltonian $H$ is self-adjoint. Sometimes, a simpler picture of the evolution…

Quantum Physics · Physics 2021-03-11 Miloslav Znojil

Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt,…

Quantum Physics · Physics 2009-11-11 Stephan I. Tzenov

All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…

Quantum Physics · Physics 2014-11-18 H. Nikolic

We argue that the conventional quantum field theory in curved spacetime has a grave drawback: The canonical commutation relations for quantum fields and conjugate momenta do not hold. Thus the conventional theory should be denounced and the…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Vladimir S. Mashkevich

In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…

Quantum Physics · Physics 2007-05-23 Pradip Kumar Chatterjee

There are fundamental reasons as to why there should exist a reformulation of quantum mechanics which does not refer to a classical spacetime manifold. It follows as a consequence that quantum mechanics as we know it is a limiting case of a…

General Relativity and Quantum Cosmology · Physics 2008-11-26 T. P. Singh

Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…

Quantum Physics · Physics 2011-02-04 Chris Fields

The solutions of the time independent Schrodinger equation for non-Hermitian (NH) Hamiltonians have been extensively studied and calculated in many different fields of physics by using L^2 methods that originally have been developed for the…

Quantum Physics · Physics 2009-11-11 Ido Gilary , Avner Fleischer , Nimrod Moiseyev

Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical…

Quantum Physics · Physics 2015-04-03 Charles Sebens

In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…

Quantum Physics · Physics 2009-11-07 H. Bergeron

In the Schroedinger formulation of non-Hermitian quantum theories a positive-definite metric operator $\eta\equiv e^{-Q}$ must be introduced in order to ensure their probabilistic interpretation. This operator also gives an equivalent…

High Energy Physics - Theory · Physics 2008-11-26 H. F. Jones , R. J. Rivers

PT-symmetric quantum mechanics is an alternative formulation of quantum mechanics in which the mathematical axiom of Hermiticity (transpose and complex conjugate) is replaced by the physically transparent condition of space-time reflection…

Mathematical Physics · Physics 2015-06-12 Huai-Xin Cao , Zhi-Hua Guo , Zheng-Li Chen

A time fractional quantum framework has been introduced into quantum mechanics. A new version of the space-time fractional Schr\"odinger equation has been launched. The introduced space-time fractional Schr\"odinger equation has a new scale…

General Physics · Physics 2017-10-11 Nick Laskin

We show that the Markovian dynamics of two coupled harmonic oscillators may be analyzed using a Schr\"odinger equation and an effective non-Hermitian Hamiltonian. This may be achieved by a non-unitary transformation that involves…

Quantum Physics · Physics 2023-04-13 L. Hernández-Sánchez , I. Ramos-Prieto , F. Soto-Eguibar , H. M. Moya-Cessa

We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with…

Quantum Physics · Physics 2009-11-10 A. Blasi , G. Scolarici , L. Solombrino

We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…

High Energy Physics - Theory · Physics 2010-02-04 Branko Dragovich , Zoran Rakic