Related papers: Time-dependent Neural Galerkin Method for Quantum …
We propose a new discrete element method supporting general polyhedral meshes. The method can be understood as a lowest-order discontinuous Galerkin method parametrized by the continuous mechanical parameters (Young's modulus and Poisson's…
The time-dependent variational principle using generalized Gaussian trial functions yields a finite dimensional approximation to the full quantum dynamics and is used in many disciplines. It is shown how these 'semi-quantum' dynamics may be…
A machine-learnable variational scheme using Gaussian radial basis functions (GRBFs) is presented and used to approximate linear problems on bounded and unbounded domains. In contrast to standard mesh-free methods, which use GRBFs to…
We study low-rank tensor methods for the numerical solution of Schr\"odinger's equation with time-independent and explicitly time-dependent Hamiltonians, motivated by large-scale simulations of many-body quantum systems and quantum…
We study the dynamics of a bounded gravitational collapsing configuration emitting gravitational waves, where the exterior spacetime is described by Robinson-Trautman geometries. The full nonlinear regime is examined by using the Galerkin…
We describe a numerical method which allows us to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent…
The problem is considered of describing the dynamics of quantum systems generated by a nonlocal in time interaction. It is shown that the use of the Feynman approach to quantum theory in combination with the canonical approach allows one to…
Recently, explicit real time dynamics has been studied in various systems. These quantum mechanical dynamics could provide new recipes in information processing. We study quantum dynamics under time dependent external fields, and explore…
We establish a generic method to analyze the time evolution of open quantum many-body systems. Our approach is based on a variational integration of the quantum master equation describing the dynamics and naturally connects to a variational…
In order to inherit numerically the ergodicity of the damped stochastic nonlinear Schr\"odinger equation with additive noise, we propose a fully discrete scheme, whose spatial direction is based on spectral Galerkin method and temporal…
Many differential equations with physical backgrounds are described as gradient systems, which are evolution equations driven by the gradient of some functionals, and such problems have energy conservation or dissipation properties. For…
We propose a general-purpose, self-adaptive approach to construct variational wavefunction ans\"atze for highly accurate quantum dynamics simulations based on McLachlan's variational principle. The key idea is to dynamically expand the…
We introduce an extension of the time-dependent variational Monte Carlo (tVMC) method that adaptively controls the expressivity of the variational quantum state during the simulation of the dynamics. This adaptive tVMC (atVMC) approach is…
Neural networks are increasingly recognized as a powerful numerical solution technique for partial differential equations (PDEs) arising in diverse scientific computing domains, including quantum many-body physics. In the context of…
A variational principle enabling one to compute individual Floquet states of a periodically time-dependent quantum system is formulated, and successfully tested against the benchmark system provided by the analytically solvable model of a…
Dynamics in correlated quantum matter is a hard problem, as its exact solution generally involves a computational effort that grows exponentially with the number of constituents. While a remarkable progress has been witnessed in recent…
In the context of Galerkin discretizations of a partial differential equation (PDE), the modes of the classical method of Proper Orthogonal Decomposition (POD) can be interpreted as the ansatz and trial functions of a low-dimensional…
In this paper, a new variational formulation based on discontinuous Galerkin technique for a reaction-diffusion problem is introduced, and the discontinuous Galerkin technique of this work is different from the general discontinuous…
Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. This approach typically relies on deep circuits and is therefore hampered by the substantial…
A dynamical quantum phase transition can occur during time evolution of sudden quenched quantum systems across a phase transition. It corresponds to the nonanalytic behavior at a critical time of the rate function of the quantum state…