Related papers: Numerical time propagation of quantum systems in r…
We show that combining ideas from the fields of quantum invariants and of optimal control can be used to design optimal quantum control solutions without explicit reference to quantum states. The states are specified only implicitly in…
By considering a solvable driven-dissipative quantum model, we demonstrate that continuous second order phase transitions in dissipative systems may occur without an accompanying spontaneous symmetry breaking. As such, the underlying…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
We present a general approach to the classical dynamical systems simulation. This approach is based on classical systems extension to quantum states. The proposed theory can be applied to analysis of multiple (including non-Hamiltonian)…
We examine an extension to the theory of Gaussian wave packet dynamics in a one-dimensional potential by means of a sequence of time dependent displacement and squeezing transformations. Exact expressions for the quantum dynamics are found,…
The necessity of rejecting the numerical model of geometrical extension is postulated on the basis of the idea of identity of space-time and physical vacuum. An attempt is made to define space-time not via the concept of manifold, but via…
We formulate a set of conditions under which dynamics of a time-dependent quantum Hamiltonian are integrable. The main requirement is the existence of a nonabelian gauge field with zero curvature in the space of system parameters. Known…
While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number…
The first part of this paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy a discrete analogue of these conditions have…
We present a numerical method to approximate the long-time asymptotic solution $\rho_\infty(t)$ to the Lindblad master equation for an open quantum system under the influence of an external drive. The proposed scheme uses perturbation…
We study the time asymptotic propagation of solutions to the reaction-diffusion cooperative systems with fractional diffusion. We prove that the propagation speed is exponential in time, and we find the precise exponent of propagation. This…
The time-dependent Schrodinger equation is solved for two model problems for a non-Hermitian quantum system.A simple matrix model system is used to examine two critical problems for these systems: complex and non-observable energies and…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schr\"odinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant.…
The explicit criterion is derived in detail for the convergence of the Magnus expansion and the existence of the Magnus solution in the interaction picture, i.e., the exponential propagator in the weakly coupled spin (I=1/2) system SnAMX...…
Driven-dissipative qubit-resonator dynamics, which are the basis of most dispersive superconducting qubit measurement schemes, are often modeled with Lindblad master equations built from subsystem local jump operators, even when the qubit…
In the scheme of a quantum nondemolition (QND) measurement, an observable is measured without perturbing its evolution. In the context of studies of decoherence in quantum computing, we examine the `open' quantum system of a two-level atom,…
The $O(N)$ stochastic propagation method, which relies on the numerical solution of the time-dependent Schr\"odinger equation using random initial states, is widely used in large-scale first-principles calculations. In this work, we…
We discuss dissipative systems in Quantum Field Theory by studying the canonical quantization of the damped harmonic oscillator (dho). We show that the set of states of the system splits into unitarily inequivalent representations of the…
Density matrices evolved according the von Neumann equation are commonly used to simulate the dynamics of driven quantum systems. However, computational methods using density matrices are often too slow to explore the large parameter spaces…