7,519 research outputs found
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
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
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.Comment: 10 pages; presented at poster session of the conference "Dynamics
Days 2003; XXIII annual conference - 4 decades of chaos 1963-2003"; September
24, 2003 - September 27, 2003; University of the Balearic Islands, Palma de
Mallorca, Spain (2003
Dynamics of complex quantum systems with energy dissipation
A complex quantum system with energy dissipation is considered. The quantum
Hamiltonians belong the complex Ginibre ensemble. The complex-valued
eigenenergies are random variables. The second differences are also complex-valued random variables. The second differences have
their real and imaginary parts and also radii (moduli) and main arguments
(angles). For =3 dimensional Ginibre ensemble the distributions of above
random variables are provided whereas for generic - dimensional Ginibre
ensemble second difference distribution is analytically calculated. The law of
homogenization of eigenergies is formulated. The analogy of Wigner and Dyson of
Coulomb gas of electric charges is studied.Comment: 4 pages; presented at poster session of the conference "Dynamics and
Statistics of Complex Systems"; May 17th, 2000 to May 18th, 2000; Max Planck
Institute for the Physics of Complex Systems; Dresden, Germany (2000
Stabilization of highly dimensional statistical systems: Girko ensemble
A quantum statistical system with energy dissipation is studied. Its
statisitics is governed by random complex-valued non-Hermitean Hamiltonians
belonging to complex Ginibre ensemble. The eigenenergies are shown to form
stable structure in thermodynamical limit (large matrix dimension limit).
Analogy of Wigner and Dyson with system of electrical charges is drawn.Comment: 5 pages; presented at poster session of the conference "Symposium on
Entropy"; June 25th, 2000 to June 28th, 2000; Max Planck Institute for the
Physics of Complex Systems; Dresden, Germany (2000
Quantum information and entropy in random matrix ensembles
The random matrix ensembles (RME), especially Gaussian random matrix
ensembles GRME and Ginibre random matrix ensembles, are applied to following
quantum 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. The distribution function for the random matrix
ensembles is derived from the maximum entropy principle. Information functional
is defined as negentropy (opposite of entropy or minus entropy).Comment: 9 pages; presented at poster session of the conference "Collective
Phenomena in the Low Temperature Physics of Glasses"; June 16, 2003 - June
20, 2003; Max Planck Institute for the Physics of Complex Systems, Dresden,
Germany (2003
Quantum anharmonic oscillator and its statistical properties in the first quantization scheme
A family of quantum anharmonic oscillators is studied in any finite spatial
dimension in the scheme of first quantization and the 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: 10 page
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.Comment: 2 pages; appeared in: "Proceedings of the XIV Polish Conference on
Computer Methods in Mechanics (PCCMM'99)", 26th May 1999- 28th May 1999,
Rzeszow, Poland, 85-86 (1999
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.Comment: 6 pages; presented at poster session of the conference "Polymorphism
in Condensed Matter International workshop"; November 13th, 2006 - November
17th, 2006; Max Planck Institute for the Physics of Complex Systems, Dresden,
Germany (2006
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