481 research outputs found
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.Comment: 9 pages; presented as talk on the conference "Polymorphism in
Condensed Matter International workshop"; November 13th, 2006 - Novemer 17th,
2006; Max Planck Institute for the Physics of Complex Systems, Dresden,
Germany (2006
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.Comment: 8 pages; presented at poster session of the conference "International
Workshop on Critical Stability of Few-Body Quantum Systems"; October 17, 2005
- October 22, 2005; Max Planck Institute for the Physics of Complex Systems,
Dresden, Germany (2005). Additional minor corrections and change
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 is considered. Each quantum system
described by is a dissipative system and the eigenenergies 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
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.Comment: 7 pages; presented at poster session of the conference "International
Workshop on Classical and Quantum Dynamical Simulations in Chemical and
Biological Physics"; June 6, 2005 - June 11, 2005; Max Planck Institute for
the Physics of Complex Systems, Dresden, Germany (2005
Discrete Hessians in study of Quantum Statistical Systems: Complex Ginibre Ensemble
The Ginibre ensemble of nonhermitean random Hamiltonian matrices is
considered. Each quantum system described by is a dissipative system and
the eigenenergies 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.Comment: 6 pages; "QP-PQ: Quantum Probability and White Noise Analysis -
Volume 13, Foundations of Probability and Physics, Proceedings of the
Conference, Vaxjo, Sweden, 25 November - 1 December 2000"; A. Khrennikov,
Ed.; World Scientific Publishers, Singapore, Vol. 13, 115-120 (2001
Complex-valued second difference as a measure of stabilization of complex dissipative statistical systems: Girko ensemble
A quantum statistical system with energy dissipation is studied. Its
statistics is governed by random complex-valued non-Hermitean Hamiltonians
belonging to complex Ginibre ensemble. The eigenenergies are shown to form
stable structure. Analogy of Wigner and Dyson with system of electrical charges
is drawn.Comment: 6 pages; "Space-time chaos: Characterization, control and
synchronization; Proceedings of the International Interdisciplinary School,
Pamplona, Spain, June 19-23, 2000"; S. Boccaletti, J. Burguete, W.
Gonzalez-Vinas, D. L. Valladares, Eds.; World Scientific Publishers,
Singapore, 45-52 (2001
An example of dissipative quantum system: finite differences for complex Ginibre ensemble
The Ginibre ensemble of complex random Hamiltonian matrices is
considered. Each quantum system described by is a dissipative system and
the eigenenergies of the Hamiltonian are complex-valued random
variables. For generic -dimensional Ginibre ensemble analytical formula for
distribution of second difference of complex eigenenergies
is presented. The distributions of real and imaginary parts of and also of its modulus and phase are provided for =3. The results
are considered in view of Wigner and Dyson's electrostatic analogy. General law
of homogenization of eigenergies for different random matrix ensembles is
formulated.Comment: 5 pages; presented at poster session of the conference "Quantum
dynamics in terms of phase-space distributions"; May 22nd, 2000 to May 26th,
2000; Max Planck Institute for the Physics of Complex Systems; Dresden,
Germany (2000
Applications of Random Matrix Ensembles in Nuclear Systems
The random matrix ensembles (RME), especially Gaussian RME and Ginibre RME,
are applied to 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.Comment: 8 pages; presented at poster session of the conference "Quantum Field
Theory in Particle and Solid State Physics"; June 2, 2003 - June 6, 2003; Max
Planck Institute for the Physics of Complex Systems, Dresden, Germany (2003
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.Comment: 7 page
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.Comment: 10 pages; presented at poster session of the conference "Motion,
sensation and self-organization in living cells"; Workshop and Seminar:
October 20, 2003 - October 31, 2003; Max Planck Institute for the Physics of
Complex Systems Dresden, Germany (2003
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.Comment: 8 pages; presented as a poster at "Computational Physics of Transport
and Interface Dynamics"; Conference and Workshop: February 18, 2002 - March
8, 2002; Max Planck Institute for the Physics of Complex Systems, Dresden,
German
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