Quantum linguistic statistics

Formulas specifying the Zipf law for frequency dictionaries are presented. Principles from which these formulas follow are discussed.     

Quantum statistics in parametric generation

The optical parametric generation is investigated in connection with the photon statistics and squeezing which are calculated in a short time approximation up to the fourth power of the interaction time.     

Quantum statistics in cosmological models

The properties and evolution of a Friedmann universe filled with a quantum gas of massless particles and massive dust are investigated on the basis of quantum statistics. Values are given for the critical temperature and the Fermi temperature, and the possibility of degeneracy of the neutrino gas is shown. The expressions obtained for the Fermi energy are applied for estimates of the neutrino density in the Universe.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 61–65, May, 1981.     

Quantum mechanical state preparation II-The statistical ensemble as a thermostat

In this sequel to an earlier paper on quantal state preparation (Park & Band, 1972), the simple model used before is adapted and somewhat generalised to enable an exact treatment of the causal evolution of a system immersed in a statistical ensemble constituted of replicas of the system itself. The ensemble is initially in a state of statistical equilibrium, but the initial state of the system is arbitrary. It is established as a purely dynamical theorem that the system is eventually coerced into the same equilibrium state as that of the replicas in the ensemble. From this general result we obtain as a special case mechanical justification for the common assumption in statistical thermodynamics that an ensemble can function as a thermostat.     

Quantum statistics of parametric amplification

Quantum statistical properties of the parametric amplification and generation are investigated. The losses are included and the pump field is treated classically. It is shown that the normal counting generating function decomposes into the product of two functions which are the generating functions for the superposition of coherent and chaotic field and that the outputting field exhibits the anticorrelation effect when the phase of incident fields fulfil a certain condition.The authors thank Mrs A.Mikulecká from Laboratory of Computer Science of Palacký University for performing computations.     

Quantum statistics of reaction-diffusion systems

A strictly quantum-statistical theory of inhomogeneous reactions is presented. The treatment is based on the theory of multi-channel reactive scattering. For the configuration probabilities of the reactants a system of reaction-diffusion equations is obtained. The expressions for the diffusion tensor and the reaction-rate coefficients are established in terms of microscopic parameters characteristic of the reacting species.     

Quantum statistics of anti-stokes luminescence

Anti-Stokes luminescence is theoretically described from the quantum statistical point of view. It is shown that this phenomenon depends on the statistical properties of the input fields. The cases of cooperative and sequential sensitization mechanisms are separately considered and the anti-Stokes generation rate terms are studied and discussed for both cases.     

Quantum particles from classical statistics

Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being “classical” or “quantum” ceases to be a basic conceptual difference. The dynamics differs, however, between quantum and classical particles. We describe position, motion and correlations of a quantum particle in terms of observables in a classical statistical ensemble. On the other side, we also construct explicitly the quantum formalism with wave function and Hamiltonian for classical particles. For a suitable time evolution of the classical probabilities and a suitable choice of observables all features of a quantum particle in a potential can be derived from classical statistics, including interference and tunneling. Besides conceptual advances, the treatment of classical and quantum particles in a common formalism could lead to interesting cross‐fertilization between classical statistics and quantum physics.     

Quantum statistics and isospin invariance

The level density of an ideal Bose or Fermi gas is written in terms of usual phase-space integrals taking isospin conservation into accoutt. This cluster decomposition includes quantum statistics corrections between equal as well as unequal charge states of the considered particles. The isospin weights are given. These results are used to formulate a simple isospin-invariant statistical bootstrap model with Bose statistics. In the framework of this model the production of neutral pions in e⁺e^? and $\text{N}\text{N}$ annihilation is investigated.     

Quantum probability and operational statistics

We develop the concept of quantum probability based on ideas of R. Feynman. The general guidelines of quantum probability are translated into rigorous mathematical definitions. We then compare the resulting framework with that of operational statistics. We discuss various relationship between measurements and define quantum stochastic processes. It is shown that quantum probability includes both conventional probability theory and traditional quantum mechanics. Discrete quantum systems, transition amplitudes, and discrete Feynman amplitudes are treated. We close with some examples that illustrate previously defined concepts.     

Quantum tunneling in ferromagnetic nanoparticles interacting with a spin thermostat: Effective Hamiltonian

An effective Hamiltonian is obtained which describes quantum tunneling in ferromagnetic nanoparticles in the presence of a hyperfine interaction of the electron spins in the nanoparticle with the microscopic spins in the environment (such as paramagnetic impurities or nuclear spins). A criterion of transition between ferromagnetic and antiferromagnetic tunneling regimes is found. The validity of the equations obtained is checked by the method of exact diagonalization. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 1, 27–32 (10 January 1998)     

Quantum statistics of multimode parametric amplification

The effect of a multimode interaction on the squeezing attainable in parametric amplification is investigated. In the non degenerate case the maximum squeezing attainable is reduced from the single mode case, whereas in the degenerate case the squeezing is essentially unaffected by the multimode nature of the interaction.     

Quantum statistics of multiphoton unimolecular dissociation

Summary We suggest a statistical model for the process of multiphoton unimolecular dissociation which considers the energy levels of the vibrational active mode, a quasi-continuous heat bath constituted by the energy levels of the remaining modes of the molecule and an electronically excited fragment resulting from the dissociation. The master equation for the system and expressions for the moments are derived and discussed in the standard second-quantization formalism. From the master equation the diagonal and off-diagonal density matrix elements are evaluated and some discussion on their applications to establish the change of light statistics is given.

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Riassunto Si suggerisce un modello statistico per il processo di dissociazione unimolecolare multifotonico che considera i livelli di energia del modo attivo vibrazionale, un bagno di calore quasi continuo costituito dai livelli di energia dei restanti modi della molecola e di un frammento eccitato elettronicamente che risulta dalla dissociazione. L’equazione master del sistema e le espressioni degl’impulsi sono derivate e discusse nel formalismo standard della seconda quantizzazione. Per l’equazione master, gli elementi di matrice della densità diagonali e al di fuori della diagonale sono calcolati e si discute sulle loro applicazioni per stabilire il cambiamento della statistica della luce.

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Резюме Мя предлагаем статистическую модель для процесса многофотонной мономолекулярной диссоциации. Эта модель учитывает энергетические уровни колебательной активной моды, энергетические квазинепрерывные уровни термостата, которые состоят из знергетических уровней оставшихся мод молекулы, и электронных возбуюдений фрагментов, образованных при диссоциации. Выводится задаюЩее уравнение для системы и выражения для моментов. Проводится обсуждение в рамках стандартного формализма вторичного квантования. С помощью задающего уравнения вычисляются диагональные и недиагональные элементы матрицы плотности. Проводится обсуюдение статистики света.

     

Quantum statistics of phonon radiations in optomechanical systems

We study the correlation statistics of phonon radiations in a weakly driven optomechanical system. Three dominated scattering processes are identified by the scattering theory analytically and the master equation numerically, whose interplay determines the phonon statistical properties. Our results show that for the large detuning, the driving field off-resonant with the system induces a small emission rate of two anti-bunched phonons. For the resonant driving field, there is a relatively large emission rate of two bunched phonons.     

Quantum statistics in a simple model of space-time

A classification of particles in two classes is proposed in the framework of a model of space-time previously introduced. One of them is constituted by particles being represented by sets of sets of preparticles. The other kind is constituted by particles represented by cuts or discontinuities in a space-time. We prove here that particles of the first and second kind follow the Bose-Einstein and Fermi-Dirac statistics, respectively.A short communication was presented at the Sanibel Symposium (Part III): On Fundamentals of Quantum Statistics and Quantum Theory, Palm Coast, Florida, March 17–20, 1980