Related papers: Effective Evolution Equations from Quantum Dynamic…
The description of quantum many-body dynamics is extremely challenging on classical computers, as it can involve many degrees of freedom. On the other hand, the time evolution of quantum states is a natural application for quantum computers…
We study the Schr\"odinger evolution generated by the Pauli-Fierz Hamiltonian, a model for nonrelativistic quantum electrodynamics, in the classical limit $\hbar \rightarrow 0$. In this regime, we rigorously derive the Newton-Maxwell…
We consider quantum dynamics of systems with fast spatial modulation of the Hamiltonian. Employing the formalism of supersymmetric quantum mechanics and decoupling fast and slow spatial oscillations we demonstrate that the effective…
We introduce a method to efficiently study the dynamical properties of many-body localized systems in the regime of strong disorder and weak interactions. Our method reproduces qualitatively and quantitatively the real-time evolution with a…
An effective operational approach to quantum mechanics is to focus on the evolution of wave-packets, for which the wave-function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of…
Simulating and predicting dynamics of quantum many-body systems is extremely challenging, even for state-of-the-art computational methods, due to the spread of entanglement across the system. However, in the long-wavelength limit, quantum…
We present an approach to simulate the Schr\"odinger equation through continuous time quantum walks. The CTQW-based simulation applies unitary evolution driven by a quantum walk to generate probability amplitude distributions at various…
Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain…
Comment on a letter to Nature Physics, where Sakmann and Kasevich claim to solve the many-body time dependent Schr\"odinger equation to simulate single experimental runs of interacting quantum systems.
We review various bounds concerning out-of-equilibrium dynamics in few-level and many-body quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical…
We characterize good clocks, which are naturally subject to fluctuations, in statistical terms. We also obtain the master equation that governs the evolution of quantum systems according to these clocks and find its general solution. This…
Solving the time-dependent quantum many-body Schr\"odinger equation is a challenging task, especially for states at a finite temperature, where the environment affects the dynamics. Most existing approximating methods are designed to…
We study the dynamics of multiparticle Carroll-Schr\"odinger (CS) quantum systems in $1{+}1$ dimensions, where $x$ acts as the evolution variable and $t$ as the configuration coordinate. We derive the $N$-body theory on equal-$x$ slices as…
The conventional, time-dependent Schroedinger equation describes only unidirectional time evolution of the state of a physical system, i.e., forward or, less commonly, backward. This paper proposes a generalized quantum dynamics for the…
We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, $D_{ab}=| \Phi_a…
In this paper, we consider the time-dependent Born-Oppenheimer approximation (BOA) of a classical quantum molecule involving a possibly large number of nuclei and electrons, described by a Schr\"odinger equation. In the spirit of Born and…
Building on recent advances in quantum algorithms which measure and reuse qubits and in efficient classical simulation leveraging projective measurements, we extend these frameworks to real-time dynamics of quantum many-body systems…
The dynamical aspects of a spin-1/2 particle in Hermitian coquaternionic quantum theory is investigated. It is shown that the time evolution exhibits three different characteristics, depending on the values of the parameters of the…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…