Related papers: Gauge P-representations for quantum-dynamical prob…
In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be…
It is shown using the Gross-Pitaevskii equation that resonance states of Bose-Einstein condensates with attractive interactions can be stabilized into true bound states. A semiclassical variational approximation and an independent quantum…
A stochastic representation of the dynamics of open quantum systems, suitable for non-perturbative system-reservoir interaction, non-Markovian effects and arbitrarily driven systems is presented. It includes the case of driving on…
In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a…
We develop an approach for the treatment of one--dimensional bounded quantum--mechanical models by straightforward modification of a successful method for unbounded ones. We apply the new approach to a simple example and show that it…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our…
We present a stochastic matter field equation for an interacting many-body Bose system in equilibrium at ultracold finite temperature. Moreover, the proposed equation can be used for non-equilibrium dynamics on phenomenological grounds.…
The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part…
Spectral methods, thanks to their high accuracy and the possibility to use fast algorithms, represent an effective way to approximate the collisional kinetic equations of Boltzmann type, such as the Boltzmann-Nordheim equation. This…
Periodic structures are ubiquitous in quantum many-body systems and quantum field theories, ranging from lattice models, compact spaces, to topological phenomena. However, previous bootstrap studies encountered technical challenges even for…
We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical…
We revisit the algebraic description of shape invariance method in one-dimensional quantum mechanics. In this note we focus on four particular examples: the Kepler problem in flat space, the Kepler problem in spherical space, the Kepler…
We introduce an approximate phase-space technique to simulate the quantum dynamics of interacting bosons. With the future goal of treating Bose-Einstein condensate systems, the method is designed for systems with a natural separation into…
We find a representation of smooth solutions to the Cauchy problem for a scalar multidimensional conservation law as small diffusion limit of a stochastic perturbation along characteristics. It helps, in particular, to study the process of…
We show how methods of number theory can be used to study anomalies in gauge quantum field theories in spacetime dimension two. To wit, the anomaly cancellation conditions for the abelian part of the local anomaly admit solutions if and…
We develop a theory of quantum fluctuations and squeezing in a three-dimensional Bose-Einstein condensate atom interferometer with nonlinear losses. We use stochastic equations in a truncated Wigner representation to treat quantum noise.…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
Stochastic quantisation is applied to the problem of calculating real-time evolution on a Minkowskian space-time lattice. We employ optimized updating using reweighting, or gauge fixing, respectively. These procedures do not affect the…
We introduce matrix quantum phase-space distributions. These extend the idea of a quantum phase-space representation via projections onto a density matrix of global symmetry variables. The method is applied to verification of low-loss…