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We formulate a systematic algorithm for constructing a whole class of Hermitian position-dependent-mass Hamiltonians which, to lowest order of perturbation theory, allow a description in terms of PT-symmetric Hamiltonians. The method is…

The short-time behavior of the survival probability of a system governed by a time-dependent non-Hermitian Hamiltonian is derived using to the second order perturbative approach. The resulting expression allows for the analysis of some…

We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians by transitioning to the interaction picture,…

We outline a procedure for applying Hamiltonian Truncation to Quantum Field Theories (QFTs) that have UV divergences. To do this, we derive a novel representation of an Effective Hamiltonian which makes manifest some of its important…

We provide a reviewlike introduction into the quantum mechanical formalism related to non-Hermitian Hamiltonian systems with real eigenvalues. Starting with the time-independent framework we explain how to determine an appropriate domain of…

Compared with time independent Hamiltonians, the dynamics of generic quantum Hamiltonians $H(t)$ are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty…

The computational complexity of time-dependent perturbation theory is well-known to be largely combinatorial whatever the chosen expansion method and family of parameters (combinatorial sequences, Goldstone and other Feynman-type…

The non-Hermitian models, which are symmetric under parity (P) and time-reversal (T) operators, are the cornerstone for the fabrication of new ultra-sensitive optoelectronic devices. However, providing the gain in such systems usually…

We reelaborate on a general method for obtaining effective Hamiltonians that describe different nonlinear optical processes. The method exploits the existence of a nonlinear deformation of the su(2) algebra that arises as the dynamical…

We propose a perturbative approach to determine the time-dependent Dyson map and the metric operator associated with time-dependent non-Hermitian Hamiltonians. We apply the method to a pair of explicitly time-dependent two dimensional…

We demonstrate that complex point transformations can be used to construct non-Hermitian first integrals, time-dependent Dyson maps and metric operators for non-Hermitian quantum systems. Initially we identify a point transformation as a…

We provide exact analytical solutions for a two dimensional explicitly time-dependent non-Hermitian quantum system. While the time-independent variant of the model studied is in the broken PT-symmetric phase for the entire range of the…

A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…

It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but…

We produce an exact solution of the Schr\"odinger equation for the generalized time dependent Swanson oscillator. The system studied is a non-Hermitian setup characterized by time dependent complex coefficients. The exact solution is…

We perform the Hamiltonian analysis for the lowest-order effective action, up to second order in derivatives, of the complete Horava theory. The model includes the invariant terms that depend on \partial_i ln N proposed by Blas, Pujolas and…

By the method of discrete transformation equations of 3-th wave hierarchy are constructed. We present in explicit form two Poisson structures, which allow to construct Hamiltonian operator consequent application of which leads to all…

We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong…

We have established that the most general form of Hamiltonian that preserves fermionic coherent states stable in time, is that of the nonstationary free fermionic oscillator. This is to be compared with the earlier result of boson coherence…

We study a non-interacting quantum particle, moving on a one-dimensional lattice, which is subjected to repetitive measurements. We investigate the consequence when such motion is interrupted and restarted from the same initial…