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We consider the problem of simulating diffusion bridges, which are diffusion processes that are conditioned to initialize and terminate at two given states. The simulation of diffusion bridges has applications in diverse scientific fields…
We have developed an efficient simulation algorithm for strongly interacting relativistic fermions in two-dimensional field theories based on a formulation as a loop gas. The loop models describing the dynamics of the fermions can be mapped…
P representation techniques, which have been very successful in quantum optics and in other fields, are also useful for general bosonic quantum dynamical many-body calculations such as Bose-Einstein condensation. We introduce a…
In strongly interacting systems with a separation of energy scales, low-energy effective Hamiltonians help provide insights into the relevant physics at low temperatures. The emergent interactions in the effective model are mediated by…
We investigate fermion--anti-fermion production in 1+1 dimensional QED using real-time lattice techniques. In this non-perturbative approach the full quantum dynamics of fermions is included while the gauge field dynamics can be accurately…
Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it.…
The stochastic solution with Gaussian stationary increments is establihsed for the symmetric space-time fractional diffusion equation when $0 < \beta < \alpha \le 2$, where $0 < \beta \le 1$ and $0 < \alpha \le 2$ are the fractional…
Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman-von Neumann formulation of classical mechanics. The Koopman-von Neumann formulation implies that the…
Solving the Fokker-Planck equation for high-dimensional complex turbulent dynamical systems is an important and practical issue. However, most traditional methods suffer from the curse of dimensionality and have difficulties in capturing…
While quantum simulation is one of the most promising applications of modern quantum devices, accessible simulation times are fundamentally limited by finite coherence times due to omnipresent noise. Based on the ideas of relational…
Simulating quantum physics with a device which itself is quantum mechanical, a notion Richard Feynman originated, would be an unparallelled computational resource. However, the universal quantum simulation of fermionic systems is daunting…
The Gaussian function (GF) is widely used to explain the behavior or statistical distribution of many natural phenomena as well as industrial processes in different disciplines of engineering and applied science. For example, the GF can be…
Lattice gauge theories are fundamental to various fields, including particle physics, condensed matter, and quantum information theory. Recent progress in the control of quantum systems allows for studying Abelian lattice gauge theories in…
Here, we develop the exact dynamics of the central spin model, modeling a finite-bath open quantum system. Particularly, two different types of interactions are investigated between the system and the bath: Heisenberg interaction with…
We analyze the many-particle Schrodinger equation for fermions in a thermal ensemble by introducing an exponential operator expansion, defined in the context of thermofield dynamics. The expansion is optimized variationally at each time…
We offer a new proposal for the Monte Carlo treatment of many-fermion systems in continuous space. It is based upon Diffusion Monte Carlo with significant modifications: correlated pairs of random walkers that carry opposite signs;…
An exact and efficient new method to simulate dynamics in dissipative quantum systems is presented. A stochastic Liouville equation, deduced from Feynman and Vernon's path-integral expression of the reduced density matrix, is used to…
Modeling dynamic, large-scale urban scenes is challenging due to their highly intricate geometric structures and unconstrained dynamics in both space and time. Prior methods often employ high-level architectural priors, separating static…
We describe numerical simulations of the critical dynamics near the superfluid phase transition. The calculations are based on an implementation of a stochastic hydrodynamic theory known as model F in the classification of Hohenberg and…
We propose a general variational fermionic many-body wavefunction that generates an effective Hamiltonian in a quadratic form, which can then be exactly solved. The theory can be constructed within the density functional theory framework,…