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Maciej M. Duras

Publications and source records attributed to Maciej M. Duras.

At least 19 recordsLinked to original sources
arXiv2019

Gaussian Random Matrix Ensembles in Phase Space

A new class of Random Matrix Ensembles is introduced. The Gaussian orthogonal, unitary, and symplectic ensembles GOE, GUE, and GSE, of random matrices are analogous to the classical Gibbs ensemble governed by Boltzmann's distribution in the coordinate space. The proposed new class of Random Matrix ensembles is an extension of the above Gaussian ensembles and it is analogous to the canonical Gibbs ensemble governed by Maxwell-Boltzmann's distribution in phase space. The thermodynamical magnitudes of partition function, intrinsic energy, free energy of Helmholtz, free energy of Gibbs, enthalpy, as well as entropy, equation of state, and heat capacities, are derived for the new ensemble. The examples of nonideal gas with quadratic potential energy as well as ideal gas of quantum matrices are provided. The distribution function for the new ensembles is derived from the maximum entropy principle.

cond-mat.stat-mech↗
arXiv2007

Quantum anharmonic oscillator and its statistical properties

In the present article a family of quantum anharmonic oscillators is studied using Hermite's function basis (Fock's basis) in the Hilbert space. The numerical investigation of the eigenenergies of that family is presented. The statistical properties of the calculated eigenvalues are compared with the theoretical predictions derived from the Random Matrix Theory. Conclusions are inferred.

cond-mat.stat-mech↗
arXiv2006

Statistical properties of the quantum anharmonic oscillator

The random matrix ensembles (RME) of Hamiltonian matrices, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applicable to following quantum statistical systems: nuclear systems, molecular systems, condensed phase systems, disordered systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). A family of quantum anharmonic oscillators is studied and the numerical investigation of their eigenenergies is presented. The statistical properties of the calculated eigenenergies are compared with the theoretical predictions inferred from the random matrix theory. Conclusions are derived.

cond-mat.stat-mech↗
arXiv2006

Statistical properties of the quantum anharmonic oscillator in one spatial dimension

The random matrix ensembles (RME) of Hamiltonian matrices, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applicable to following quantum statistical systems: nuclear systems, molecular systems, condensed phase systems, disordered systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). A family of quantum anharmonic oscillators in one spatial dimension is studied and the numerical investigation of their eigenenergies is presented. The statistical properties of the calculated eigenenergies are compared with the theoretical predictions inferred from the random matrix theory. Conclusions are derived.

cond-mat.stat-mech↗
arXiv2005

Quantum fluctuations of systems of interacting electrons in two spatial dimensions

The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear systems, molecular systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum integrability with respect to eigenergies of quantum systems are defined and calculated. Quantum statistical information functional is defined as negentropy (opposite of entropy or minus entropy). The distribution function for the random matrix ensembles is derived from the maximum entropy principle.

cond-mat.stat-mech↗
arXiv2005

Simulations of fluctuations of quantum statistical systems of electrons

The random matrix ensembles (RMT) of quantum statistical Hamiltonian operators, e.g.Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear systems, molecular systems, and two-dimensional electron systems (Wigner-Dyson's electrostatic analogy). 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 second difference of complex eigenenergies is viewed as discrete analog of Hessian with respect to labelling index. The results are considered in view of Wigner and Dyson's electrostatic analogy. An extension of space of dynamics of random magnitudes is performed by introduction of discrete space of labeling indices. The comparison with the Gaussian ensembles of random hermitean Hamiltonian matrices $H$ is performed. Measures of quantum chaos and quantum integrability with respect to eigenergies of quantum systems are defined and they are calculated. Quantum statistical information functional is defined as negentropy (opposite of von Neumann's entropy or minus entropy). The probability distribution functionals for the random matrix ensembles (RMT) are derived from the maximum entropy principle.

cond-mat.stat-mech↗
arXiv2005

Fluctuations of Quantum Statistical Two-Dimensional Systems of Electrons

The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear systems, molecular systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum integrability with respect to eigenergies of quantum systems are defined and calculated. Quantum statistical information functional is defined as negentropy (either opposite of entropy or minus entropy). The distribution function for the random matrix ensembles is derived from the maximum entropy principle.

cond-mat.stat-mech↗
arXiv2004

Information functional for quantum random matrix ensembles

Random matrix ensembles (RME) of quantal statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), had been applied in literature in study of following quantal statistical systems: molecular systems, nuclear systems, disordered materials, random Ising spin systems, quantal chaotic systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum integrability with respect to eigenergies of quantal systems are defined and calculated. Information functional is defined as negentropy (opposite of entropy or minus entropy). Entropy is neginformation (opposite of information or minus information. The distribution functions for the random matrix ensembles are derived from the maximum entropy principle.

cond-mat.stat-mech↗
arXiv2004

Maximum entropy principle and quantum statistical information functional in random matrix ensembles

The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear systems, molecular systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum integrability with respect to eigenergies of quantum systems are defined and calculated. Quantum statistical information functional is defined as negentropy (opposite of entropy or minus entropy). The distribution function for the random matrix ensembles is derived from the maximum entropy principle.

cond-mat.stat-mech↗
arXiv2003

Quantum statistical information, entropy, Maximum Entropy Principle in various quantum random matrix ensembles

Random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), found applications in literature in study of following quantum statistical systems: molecular systems, nuclear systems, disordered materials, random Ising spin systems, quantum chaotic systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum integrability with respect to eigenergies of quantum systems are defined and calculated. Quantum statistical information functional is defined as negentropy (opposite of entropy or minus entropy). Entropy is neginformation (opposite of information or minus information. The distribution functions for the random matrix ensembles are derived from the maximum entropy principle.

cond-mat.stat-mech↗
arXiv2003

Entropy, Maximum Entropy Priciple and quantum statistical information for various random matrix ensembles

The random matrix ensembles (RME) of quantum statistical Hamiltonians, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied in literature to following quantum statistical systems: molecular systems, nuclear systems, disordered materials, random Ising spin systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum integrability with respect to eigenergies of quantum systems are defined and calculated. Quantum statistical information functional is defined as negentropy (opposite of entropy or minus entropy). Entropy is neginformation (opposite of information or minus information. The distribution functions for the random matrix ensembles are derived from the maximum entropy principle.

cond-mat.stat-mech↗
arXiv2003

Applications of methods of quantum statistical mechanics to two-dimensional electron systems

The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the systems act on these Hilbert spaces and they are treated as random matrices in generic bases of the eigenfunctions. The random eigenproblems are presented and solved. Examples of random operators are presented with connection to physical problems.

cond-mat.stat-mech↗
arXiv2003

Finite-difference distributions for the Ginibre ensemble

The Ginibre ensemble of complex random matrices is studied. The complex valued random variable of second difference of complex energy levels is defined. For the N=3 dimensional ensemble are calculated distributions of second difference, of real and imaginary parts of second difference, as well as of its radius and of its argument (angle). For the generic N-dimensional Ginibre ensemble an exact analytical formula for second difference's distribution is derived. The comparison with real valued random variable of second difference of adjacent real valued energy levels for Gaussian orthogonal, unitary, and symplectic, ensemble of random matrices as well as for Poisson ensemble is provided.

cond-mat.stat-mech↗
arXiv2003

Urban tranport phenomena in the street canyon

A field deterministic model of the vehicular dynamics in a generic urban street canyon with two neighboring canyons is considered. The assumed hydrodynamical model of vehicular movement is coupled to the gasdynamical model of the air and emitted pollutants. The vehicles are assumed to move on distinct left lanes and right ones. At the upstream and downstream ends there are coordinated traffic lights which introduce control parameters to the field model. The model of optimal control of street canyon dynamics is based on the two optimal multi-criteria control problems. The problems consist of minimization of the dimensionless functionals of the cumulative total travel time, global emissions of pollutants, and global concentrations of pollutants, both in the studied street canyon, as well as together with the two nearest neighbor substitute canyons, respectively.

cond-mat.dis-nn↗
arXiv2003

Gasdynamic model of street canyon

A general proecological urban road traffic control idea for the street canyon is proposed with emphasis placed on development of advanced continuum field gasdynamical (hydrodynamical) control model of the street canyon. The continuum field model of optimal control of street canyon is studied. The mathematical physics approach (Eulerian approach) to vehicular movement, to pollutants' emission and to pollutants' dynamics is used. The rigorous mathematical model is presented, using gasdynamical (hydrodynamical) theory for both air constituents and vehicles, including many types of vehicles and many types of pollutant (exhaust gases) emitted from vehicles. The six optimal control problems are formulated and numerical simulations are performed. Comparison with measurements are provided. General traffic engineering conclusions are inferred.

cond-mat.dis-nn↗
arXiv2003

Description of Quantum Systems by Random Matrix Ensembles of High Dimensions

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 ensemble GUE($N$), $N$-dimensional Gaussian symplectic ensemble GSE($N$), and Poisson ensemble PE, is formulated: {\it The probability density functions of the dimensionless second difference of the three adjacent energy levels take on maximum at the origin for the following ensembles: GOE($N$), GUE($N$), GSE($N$), and PE, where $N \geq 3$.} The notions of {\it level homogenization with level clustering} and {\it level homogenization with level repulsion} are introduced.

cond-mat.stat-mech↗
arXiv2003

Transport phenomena in the urban street canyon

A generic proecological traffic control model for the urban street canyon is proposed by development of advanced continuum field hydrodynamical control model of the street canyon. The model of optimal control of street canyon dynamics is also investigated. The mathematical physics' approach (Eulerian approach) to vehicular movement, to pollutants' emission, and to pollutants' dynamics is used. The rigorous mathematical model is presented, using hydrodynamical theory for both air constituents and vehicles, including many types of vehicles and many types of pollutants emitted from vehicles. The six proposed optimal monocriterial control problems consist of minimization of functionals of the total travel time, of global emissions of pollutants, and of global concentrations of pollutants, both in the studied street canyon, and in its two nearest neighbour substitute canyons, respectively. The six optimization problems are solved numerically. Generic traffic control issues are inferred. The discretization method, comparison with experiment, mathematical issues, and programming issues are discussed.

cond-mat.dis-nn↗