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In 1931/32, Schroedinger studied a hot gas Gedankenexperiment, an instance of large deviations of the empirical distribution and an early example of the so-called maximum entropy inference method. This so-called Schroedinger bridge problem…
The Pade approximant technique and the variational Monte Carlo method are applied to determine the ground-state energy of a finite number of charged bosons in two dimensions confined by a parabolic trap. The particles interact repulsively…
These notes deal with the mean-field approximation for equilibrium states of N-body systems in classical and quantum statistical mechanics. A general strategy for the justification of effective models based on statistical independence…
Estimating the ground-state energy of Hamiltonians is a fundamental task for which it is believed that quantum computers can be helpful. Several approaches have been proposed toward this goal, including algorithms based on quantum phase…
We analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be…
Elementary introduction to the application of Mathematica 3.0 to the solution of bound-state problems in quantum theory by standard variational procedures, with particular emphasis on the computation of precise upper bounds on energy levels…
In this paper we consider the three dimensional exterior Stokes problem and study the solvability of the corresponding continuous and discrete formulations that arise from the coupling of a dual-mixed variational formulation with the…
By means of a generalized quartet mechanism we show in a model independent way that a BRST quantization on an inner product space leads to physical states of the form |ph>=e^{[Q, \psi]} |ph>_0 where Q is the nilpotent BRST operator, \psi a…
From a covariant Hamiltonian formulation, using symplectic ideas, we obtain covariant quasilocal energy-momentum boundary expressions for general gravity theories. The expressions depend upon which variables are fixed on the boundary, a…
We study the corrections to the fine-structure constant from the generalized uncertainty principle in the spacetime of a domain wall. We also calculate the corrections to the standard formula to the energy of the electron in the hydrogen…
In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed in a generalized sense. The applications included the…
Simple analytical parametrizations for the ground-state energy of the one-dimensional repulsive Hubbard model are developed. The charge-dependence of the energy is parametrized using exact results extracted from the Bethe-Ansatz. The…
Podolsky's electromagnetism which explains some of unresolved problems of usual QED has been investigated in the framework of finite field dependent (FFBRST) BRST transformation. In this generalized QED (GQED), BRST invariant effective…
Reliable and efficient computation of the pseudospectral abscissa in the large-scale setting is still not settled. Unlike the small-scale setting where there are globally convergent criss-cross algorithms, all algorithms in the large-scale…
Techniques to reduce the energy burden of an industrial ecosystem often require solving a multiobjective optimization problem. However, collecting experimental data can often be either expensive or time-consuming. In such cases, statistical…
For a quantum mechanical system with broken supersymmetry, we present a simple method of determining the ground state when the corresponding energy eigenvalue is sufficiently small. A concise formula is derived for the approximate ground…
The general idea to modify Einstein's field equations by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$ was apparently outlined for the first time in [12-15]. The modification itself originates from…
Variational methods play an important role in the study of quantum many-body problems, both in the flavor of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum…
The recent observational data in cosmology seem to indicate that the universe is currently expanding in an accelerated way. An intriguing interpretation of these data is that they may just be signalling that Einstein's General Relativity is…
Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert…