Related papers: Universal Hamiltonians for Exponentially Long Simu…
An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the…
A novel scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. The idea is to consider a certain open-system evolution,…
Current studies about the continuous-variable systems in non-Hermitian quantum mechanics heavily revolved around the singularities in the eigenspectrum by mimicking their discrete-variable counterparts. Discussions over the nonunitary…
We consider quantum systems with causal dynamics in discrete spacetimes, also known as quantum cellular automata (QCA). Due to time-discreteness this type of dynamics is not characterized by a Hamiltonian but by a one-time-step unitary.…
Classical simulation of quantum systems plays an important role in the study of many-body phenomena and in the benchmarking and verification of quantum technologies. Exact simulation is often limited to small systems because the dimension…
We develop a Hamiltonian theory of a time dispersive and dissipative inhomogeneous medium, as described by a linear response equation respecting causality and power dissipation. The proposed Hamiltonian couples the given system to auxiliary…
The temporal evolution of the entanglement between two qubits evolving by random interactions is studied analytically and numerically. Two different types of randomness are investigated. Firstly we analyze an ensemble of systems with…
A system of a quantum harmonic oscillator bi-linearly coupled with a Glauber amplifier is analysed considering a time-dependent Hamiltonian model. The Hilbert space of this system may be exactly subdivided into invariant finite dimensional…
In a recent paper, Hassoul et al.[1], the authors proposed an analysis of the quantum dynamics for general time-dependent three coupled oscillators through an approach based on their decouplement using the unitary transformation method.…
The dynamical evolution of an open quantum system can be governed by the Lindblad equation of the density matrix. In this paper, we propose to characterize the density matrix topology by the topological invariant of its modular Hamiltonian.…
Hamilton's principle is extended to have compatible initial conditions to the strong form. To use a number of computational and theoretical benefits for dynamical systems, the mixed variational formulation is preferred in the systems other…
We study four particular 3-dimensional natural Hamiltonian systems defined in conformally Euclidean spaces. We prove their superintegrability and we obtain, in the four cases, the maximal number of functionally independent integrals of…
We consider quantum systems which interact strongly with a rapidly varying environment and derive a Schrodinger-like equation which describes the time evolution of the average wave function. We show that the corresponding Hamiltonian can be…
We study the time evolution of the amount of entanglement generated by one dimensional spin-1/2 Ising-type Hamiltonians composed of many-body interactions. We investigate sets of states randomly selected during the time evolution generated…
We investigate the inverse problem concerning the evolution of a qubit system, specifically we consider how one can establish the Hamiltonians that account for the evolution of a qubit along a prescribed path in the projected Hilbert space.…
The Floquet-Magnus expansion is a useful tool to calculate an effective Hamiltonian for periodically driven systems. In this study, we investigate the convergence of the expansion for a one-body nonlinear system in a continuous space, a…
In this paper, we study evolutive Hamilton Jacobi equations with Hamiltonians that are discontinuous in time, posed on a simple network consisting of two edges on the real line connected at a single junction. We introduce a notion of…
For a large class of time-dependent non-Hermitain Hamiltonians expressed in terms linear and bilinear combinations of the generators for an Euclidean Lie-algebra respecting different types of PT-symmetries, we find explicit solutions to the…
In this paper we propose a new supersymmetric extension of conformal mechanics. The Grassmannian variables that we introduce are the basis of the forms and of the vector-fields built over the symplectic space of the original system. Our…
The problem of simulating sparse Hamiltonians on quantum computers is well studied. The evolution of a sparse N x N Hamiltonian H for time t can be simulated using O(||Ht||poly(log N)) operations, which is essentially optimal due to a…