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Years ago Edwards proposed a thermodynamic description of dense granular matter, in which the grains (the `atoms' of the system) interact with inelastic forces. The approach is intriguing but is not justified from first principles, and…
The entropy of a de Sitter horizon was derived long ago by Gibbons and Hawking via a gravitational partition function. Since there is no boundary at which to define the temperature or energy of the ensemble, the statistical foundation of…
We present a hybrid asymptotic/numerical method for the accurate computation of single and double layer heat potentials in two dimensions. It has been shown in previous work that simple quadrature schemes suffer from a phenomenon called…
Symplectic integrators are widely used for long-term integration of conservative astrophysical problems due to their ability to preserve the constants of motion; however, they cannot in general be applied in the presence of nonconservative…
The Generalized Langevin Equation (GLE) has been recently suggested to simulate the time evolution of classical solid and molecular systems when considering general non-equilibrium processes. In this approach, a part of the whole system (an…
Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the…
We introduce a method that ensures efficient computation of one-dimensional quantum systems with long-range interactions across all temperatures. Our algorithm operates within a quasi-polynomial runtime for inverse temperatures up to…
Quantum simulators, in which well controlled quantum systems are used to reproduce the dynamics of less understood ones, have the potential to explore physics that is inaccessible to modeling with classical computers. However, checking the…
We present a boundary integral method for numerical computation of the capacity of generalized condensers. The presented method applies to a wide variety of generalized condenser geometry including the cases when the plates of the…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that…
We show that the infinite-dimensional representation of the recently introduced Logistic algebra can be interpreted as a non-trivial generalization of the Heisenberg or oscillator algebra. This allow us to construct a quantum Hamiltonian…
Structure-preserving integrators are in the focus of ongoing research because of their distinguished features of robustness and long time stability. In particular, their formulation for coupled problems that include dissipative mechanisms…
We introduce a hybrid classical-quantum algorithm to compute dynamical correlation functions and excitation spectra in many-body quantum systems, with a focus on molecular systems. The method combines classical preparation of a perturbed…
Molecular dynamics with the stochastic process provides a convenient way to compute structural and thermodynamic properties of chemical, biological, and materials systems. It is demonstrated that the virtual dynamics case that we proposed…
The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practicaltechniques for the simulation of solids. Monte Carlo and molecular dynamics methods for…
We discuss a new Monte Carlo algorithm for the simulation of complex fluids. This algorithm employs geometric operations to identify clusters of particles that can be moved in a rejection-free way. It is demonstrated that this geometric…
We review the main aspects of geometrothermodynamics, a formalism that uses contact geometry and Riemannian geometry to describe the properties of thermodynamic systems. We show how to handle in a geometric way the invariance of classical…
We present an efficient strategy for controlling a vast range of non-integrable quantum many body one-dimensional systems that can be merged with state-of-the-art tensor network simulation methods like the density Matrix Renormalization…
As is well known, energy is generally deemed as one of the most important physical invariants in many conservative problems and hence it is of remarkable interest to consider numerical methods which are able to preserve it. In this paper,…