Related papers: Operators for the Aharonov-Anandan and Samuel-Bhan…
In this work we intend to study a class of time-dependent quantum systems with non-Hermitian Hamiltonians, particularly those whose Hermitian counterpart are important for the comprehension of posed problems in quantum optics and quantum…
Quantum timeless approaches solve the problem of time by recovering the usual unitary evolution of quantum theory relative to a clock in a stationary quantum Universe. For some Hamiltonians of the Universe, such as those including an…
We introduce a general framework for realizing $\mathcal{PT}$-like phase transitions in non-Hermitian systems without imposing explicit parity--time ($\mathcal{PT}$) symmetry. The approach is based on constructing a Hamiltonian as the…
Geometric phase is a concept of central importance in virtually every branch of physics. In this paper, we show that the evolution time of a cyclically evolving quantum system is restricted by the system's energy resources and the geometric…
Quantum systems governed by time-dependent Hamiltonians pose significant challenges for the accurate computation of unitary time-evolution operators, which are essential for predicting quantum state dynamics. In this work, we introduce a…
The evolution equations of quantum observables are derived from the classical Hamiltonian equations of motion with the only additional assumption that the phase space is non-commutative. The demonstration of the quantum evolution laws is…
By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with…
We develop a mathematical framework for quantum time transfer based on commuting families of Hamiltonians and synchronization observables. The synchronization subspace is defined as the kernel of a difference operator between local clocks,…
We introduce a one-parameter generalized oscillator algebra A(k) (that covers the case of the harmonic oscillator algebra) and discuss its finite- and infinite-dimensional representations according to the sign of the parameter k. We define…
We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…
The correspondence between classical and quantum invariants is established. The Ermakov Lewis quantum invariant of the time dependent harmonic oscillator is translated from the coordinate and momentum operators into amplitude and phase…
In this paper we develop an analogue of Hamilton-Jacobi theory for the time-evolution operator of a quantum many-particle system. The theory offers a useful approach to develop approximations to the time-evolution operator, and also…
We study quantum decoherence of single-qubit and two-qubit Aharonov-Anandan (AA) geometric phase gates realized in a multistep scheme. Each AA gate is also compared with the dynamical phase gate performing the same unitary transformation…
A non-Hermitian operator $H$ defined in a Hilbert space with inner product $\langle\cdot|\cdot\rangle$ may serve as the Hamiltonian for a unitary quantum system, if it is $\eta$-pseudo-Hermitian for a metric operator (positive-definite…
Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and…
Within the framework of self-adjoint operator of time in non-relativistic quantum mechanics some properties of solutions of Schroedinger equation, related to Hilbert space formalism, are investigated for two types of time dependent…
We study the total (dynamical plus geometrical (Berry)) phase of cyclic quantum motion for coherent states over homogeneous K\"ahler manifolds X=G/H, which can be considered as the phase spaces of classical systems and which are, in…
Describing systems with non-Hermitian (NH) operators remains a challenge in quantum theory due to instabilities (e.g., exceptional points and decoherence) arising from interactions with the environment. We propose a framework to express the…
The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…
We apply the method of flow equations to describe quantum systems subject to a time-periodic drive with a time-dependent envelope. The driven Hamiltonian is expressed in terms of its constituent Fourier harmonics with amplitudes that may…