Related papers: Modified Hellmann Feynman Theorem
Non-radiative wireless power transfer (WPT) technology has made considerable progress with the application of the parity-time (PT) symmetry concept. In this letter, we extend the standard second-order PT-symmetric Hamiltonian to high-order…
The Hellmann-Feynman (HF) theorem provides a way to compute forces directly from the electron density, enabling efficient force calculations for large systems through machine learning (ML) models for the electron density. The main issue…
A TQFT in terms of general gauge fixing functions is discussed. In a covariant gauge it yields the Donaldson-Witten TQFT. The theory is formulated on a generalized phase space where a simplectic structure is introduced. The Hamiltonian is…
In the context of quasi-Hermitian theories, which are non-Hermitian in the conventional sense, but can be made Hermitian by the introduction of a dynamically-determined metric $\eta$, we address the problem of how the functional integral…
Update: A time-independent $n\times n$ PT-symmetric (and symmetric) Hamiltonian is diagonalizable since it has all distinct real eigenvalues and the resulting diagonal matrix is a real symmetric matrix. The diagonalization results an…
We present a mathematical formalism of non-Hermitian quantum mechanics, following the Dirac-von Neumann formalism of quantum mechanics. In this formalism, the state postulate is the same as in the Dirac-von Neumann formalism, but the…
Given an initial quantum state |psi_I> and a final quantum state |psi_F> in a Hilbert space, there exist Hamiltonians H under which |psi_I> evolves into |psi_F>. Consider the following quantum brachistochrone problem: Subject to the…
We show that degenerate four-wave mixing (FWM) in nonlinear optics can be described by an effective Hamiltonian that is pseudo-Hermitian, which enables a transition between a pseudo-Hermitian phase with real eigenvalues and a broken…
There is growing interest in viable quantum theories with PT-symmetric non-Hermitian Hamiltonians, but a formulation of transition matrix elements consistent with positivity and perturbative unitarity has so far proved elusive. This Letter…
While Hermiticity of a time-independent Hamiltonian leads to unitary time evolution, in and of itself, the requirement of Hermiticity is only sufficient for unitary time evolution. In this paper we provide conditions that are both necessary…
For any pair of quantum states, an initial state |I> and a final quantum state |F>, in a Hilbert space, there are many Hamiltonians H under which |I> evolves into |F>. Let us impose the constraint that the difference between the largest and…
In this work, we investigate many-body phase transitions in a one-dimensional anisotropic XY model subject to a complex-valued transverse field. Within the biorthogonal framework, we calculate the ground-state correlation functions and…
In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully…
Explicitly time-dependent pseudo-Hermitian (TDPH) invariants theory systems, with a time-dependent (TD) metric, is developed for a time-dependent non Hermitian (TDNH) quantum systems. We derive a simple relation between the eigenstates of…
A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum…
Non-Hermitian quantum systems exhibit fascinating characteristics such as non-Hermitian topological phenomena and skin effect, yet their studies are limited by the intrinsic difficulties associated with their eigenvalue problems, especially…
Quantum inverse problem is defined as how to determine a local Hamiltonian from a single eigenstate? This question is valid not only in Hermitian system but also in non-Hermitian system. So far, most attempts are limited to Hermitian…
Quantum mechanics of unitary systems is considered in quasi-Hermitian representation. In this framework the concept of perturbation is found counterintuitive, for three reasons. The first one is that in this formalism we are allowed to…
Quantum physics is generally concerned with real eigenvalues due to the unitarity of time evolution. With the introduction of $\mathcal{PT}$ symmetry, a widely accepted consensus is that, even if the Hamiltonian of the system is not…
In the context of two particularly interesting non-Hermitian models in quantum mechanics we explore the relationship between the original Hamiltonian H and its Hermitian counterpart h, obtained from H by a similarity transformation, as…