Related papers: Multi-particle quantum systems within the Worldlin…
In this Ph.D. thesis quantum Monte Carlo methods are applied to investigate the properties of a number of ultracold quantum systems. In Chapter 1 we discuss the analytical approaches and approximations used in the subsequent Chapters; also…
We present a quantum Monte Carlo method capable of sampling the full density matrix of a many-particle system at finite temperature. This allows arbitrary reduced density matrix elements and expectation values of complicated non-local…
The discrete time path integral Monte Carlo (PIMC) with a one-particle density matrix approximation is applied to study the quantum phase transition in the coupled double-well chain. To improve the convergence properties, the exact action…
In quantum information theory, there is an explicit mapping between general unitary dynamics and Hermitian ground state eigenvalue problems known as the Feynman-Kitaev Clock. A prominent family of methods for the study of quantum ground…
Recently a new formulation of quantum mechanics has been introduced, based on signed classical field-less particles interacting with an external field by means of only creation and annihilation events. In this paper, we extend this novel…
In nuclear fusion and fission, fluctuation and dissipation arise due to the coupling of collective degrees of freedom with internal excitations. Close to the barrier, both quantum, statistical and non-Markovian effects are expected to be…
The standard approach for path integral Monte Carlo simulations of open quantum systems is extended as an efficient tool to monitor the time evolution of coherences (off-diagonal elements of the reduced density matrix) also for strong…
We present results for a variety of Monte Carlo annealing approaches, both classical and quantum, benchmarked against one another for the textbook optimization exercise of a simple one-dimensional double-well. In classical (thermal)…
We present a new approach based on real time domain Feynman path integrals (RTPI) for electronic structure calculations and quantum dynamics, which includes correlations between particles exactly but within the numerical accuracy. We…
We discuss finite temperature quantum Monte Carlo methods in the framework of the interacting nuclear shell model. The methods are based on a representation of the imaginary-time many-body propagator as a superposition of one-body…
The auxiliary-field quantum Monte Carlo (AFQMC) method is a general numerical method for correlated many-electron systems, which is being increasingly applied in lattice models, atoms, molecules, and solids. Here we introduce the theory and…
A simple reweighting scheme is proposed for Monte Carlo simulations of interacting particle systems, permitting one to study various parameter values in a single study, and improving efficiency by an order of magnitude. Unlike earlier…
High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…
In this work we introduce a worldline based fermion Monte Carlo algorithm for studying few body quantum mechanics of self-interacting fermions in the Hamiltonian lattice formulation. Our motivation to construct the method comes from our…
In this paper, we propose a general analysis framework for inexact power iteration, which can be used to efficiently solve high dimensional eigenvalue problems arising from quantum many-body problems. Under the proposed framework, we…
The Feynman path integral has revolutionized modern approaches to quantum physics. Although the path integral formalism has proven very successful and spawned several approximation schemes, the direct evaluation of real-time path integrals…
We show how one can compute multiple-time multi-particle correlation functions in nonlinear quantum mechanics in a way which guarantees locality of the formalism.
Monte Carlo simulations of lattice quantum field theories on Lefschetz thimbles are non trivial. We discuss a new Monte Carlo algorithm based on the idea of computing contributions to the functional integral which come from complete flow…
We briefly review the principles, mathematical bases, numerical shortcuts and applications of fast random walk (FRW) algorithms. This Monte Carlo technique allows one to simulate individual trajectories of diffusing particles in order to…
We provide a worldline representation of the one-loop effective action for a Dirac particle coupled to external scalar, pseudoscalar, vector and axialvector fields. Extending previous work by two of the authors on the pure…