Related papers: Determinism plus chance in random matrix theory
Randomness is viewed through an analogy between a physical quantity, density of gas, and a mathematical construct -- probability density. Boltzmann's deduction of equilibrium distribution of ideal gas placed in an external potential field…
The new Theorem on location of maximum of probability density functions of dimensionless second difference of the three adjacent energy levels for $N$-dimensional Gaussian orthogonal ensemble GOE($N$), $N$-dimensional Gaussian unitary…
Consider a deterministic self-adjoint matrix X_n with spectral measure converging to a compactly supported probability measure, the largest and smallest eigenvalues converging to the edges of the limiting measure. We perturb this matrix by…
We compute the survival probability of an initial state, with an energy in a certain window, by means of random matrix theory. We determine its probability distribution and show that is is universal, i.e. caracterised only by the symmetry…
We developed a deep generative model-based variational free energy approach to the equations of state of dense hydrogen. We employ a normalizing flow network to model the proton Boltzmann distribution and a fermionic neural network to model…
An algebraic procedure to find extremal density matrices for any Hamiltonian of a qudit system is established. The extremal density matrices for pure states provide a complete description of the system, that is, the energy spectra of the…
A method of resummation of infinite series of perturbation theory diagrams is applied for studying the properties of random band matrices. The topological classification of Feynman diagrams, which was actively used in last years for matrix…
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…
The present article introduces a generalization of the (multisymplectic) Hamiltonian field theory for a Lagrangian density, allowing the formulation of this kind of field theories for variational problem of more general nature than those…
We develop a statistical method to learn a molecular Hamiltonian matrix from a time-series of electron density matrices. We extend our previous method to larger molecular systems by incorporating physical properties to reduce…
We study operators obtained by coupling an $n \times n$ random matrix from one of the Gaussian ensembles to the discrete Laplacian. We find the joint distribution of the eigenvalues and resonances of such operators. This is one of the…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques. Here, we present a…
We have extended the density matrix renormalization group (DMRG) approach to two-fluid open many-fermion systems governed by complex-symmetric Hamiltonians. The applications are carried out for three- and four-nucleon (proton-neutron)…
By using a recently proposed probabilistic approach, we determine the exact ground state of a class of matrix Hamiltonian models characterized by the fact that in the thermodynamic limit the multiplicities of the potential values assumed by…
The Ginibre ensemble of nonhermitean random Hamiltonian matrices $K$ is considered. Each quantum system described by $K$ is a dissipative system and the eigenenergies $Z_{i}$ of the Hamiltonian are complex-valued random variables. The…
In order to extend the density-matrix renormalization-group (DMRG) method to two-dimensional systems, we formulate two alternative methods to prepare the initial states. We find that the number of states that is needed for accurate energy…
We explicitly calculate Janossy densities for a special class of finite determinantal point processes with several types of particles introduced by Pr\"ahofer and Spohn and, in the full generality, by Johansson in connection with the…
In this thesis, we consider several Random Energy Models. This includes Derrida's Random Energy Model (REM) and Generalized Random Energy Model (GREM) and a nonhierarchical version (BK-GREM) by Bolthausen and Kistler. The limiting free…
We study the dynamics of particles coupled to gravity in (2 + 1) dimensions. Using the ADM formalism, we derive the general Hamiltonian for an N-body system and analyze the dynamics of a two-particle system. Non-linear terms are found up to…