Increase of temperature of an ideal nondegenerate quantum gas in a suddenly expanding box due to energy quantization

We show that due to energy quantization the temperature of an ideal nondegenerate quantum gas in a rectangular box always increases after a sudden expansion of the box and a subsequent thermalization. The maximal increment of temperature is proportional to the square root of the product of the initial absolute temperature by the energy of the first discrete quantum level, i.e., it is proportional to the first power of the Planck constant.     

High-probability quantum state transfer among nodes of an open XXZ spin chain

This Letter concerns the problem of the high probability state transfer among s² symmetrically placed nodes of the N-node chain of spins 1/2 with the XXZ Hamiltonian. We consider examples with (N,s)=(4,4), (N,s)=(6,4) and (N,s)=(8,8).     

General kinetic equation and irreversibility in statistical systems

General kinetic equation for statistical systems is presented. A kinetic equation with source that is fluctuation of physical values was obtained. A new statistical criterion of systems evolution was determined. Nonequilibrium statistical and variational derivations of general kinetic equations are considered. Evolution of nonequilibrium Boltzmann-Gibbs-Shannon entropy, Hamilton function and Hamilton function production are examined.     

High-probability quantum state transfer in an alternating open spin chain with an XY Hamiltonian

This Letter concerns the problem of non-ideal state transfer along the alternating open chain of spins s=1/2 with the XY Hamiltonian. It is found that the state transfer along the chain with even number of spins N (N=4,6,8) may be realized with high probability. Privilege of even N in comparison with odd N is demonstrated.     

Statistical Interaction Term of One-Dimensional Anyon Models

A form of statistical interaction term of one-dimensional anyons is introduced, based on which one-dimensional anyon models are theoretically realized, and the statistical transmutation between bosons （or fermions） and anyons is established in quantum mechanics formalism. Two kinds of anyon models which are being studied are recovered and reexplained naturally in our formalism.     

Fractional exclusion statistics in general systems of interacting particles

I show that fractional exclusion statistics is manifested in general interacting systems and I calculate the exclusion statistics parameters. Most importantly, I prove that the mutual exclusion statistics parameters are proportional to the dimension of the Hilbert space on which they act [D.V. Anghel, J. Phys. A: Math. Theor. 40 (2007) F1013].     

A decomposed equation for local entropy and entropy production in volume-preserving coarse-grained systems

In this study an equation for the local entropy is derived based on the formulation of a master equation and is applied to volume-preserving maps. The equation consists of the following terms: unsteady, convection, diffusion, probability-weighted phase space volume expansion rate, nonnegative entropy production, and residuals. The decomposition makes it possible to evaluate entropy production in terms of microscopic dynamics and is expected to be applicable to many coarse-grained systems on the phase space. When it is applied to two volume-preserving multibaker chain systems it is confirmed that the summation of the nonnegative entropy production on each site numerically coincides with the entropy production introduced by Gilbert et al. [T. Gilbert, J.R. Dorfman, P. Gaspard, Entropy production, fractals, and relaxation to equilibrium, Phys. Rev. Lett. 85 (2000) 1606-1609] and the phenomenological expression both in nonequilibrium steady and unsteady states. The coincidence is brought about by the fact that the residual terms vanish in the thermodynamic limit when they are integrated on each site. It follows that the entropy production is dominated by the nonnegative entropy production term and becomes positive in nonequilibrium states.     

Conclusive and perfect quantum state transfer with a single spin chain

We have investigated the quantum state transfer in randomly coupled spin chains. By using local memories storing the information and dividing the process into transfer and decoding, conclusive transfer is spontaneously achieved with just one single spin chain. Especially, we can decode information from memories without adding extra spin chain. Compared with Time-reversed protocol, the average decoding time is much less in our scheme.     

First-order density matrices in one dimension for independent fermions and impenetrable bosons in harmonic traps

To complement existing knowledge of the density matrix γF(x,y)${\gamma }_{\mathrm{F}}(x,y)$ of independent fermions for N   particles in one dimension under harmonic confinement, the corresponding matrix γIB(x,y)${\gamma }_{\mathrm{IB}}(x,y)$ for impenetrable bosons is given for N=2$N=2$ and 3 (with the N=4$N=4$ form available also). For fermions the momentum density is then obtained and illustrated numerically for N=10$N=10$. The boson momentum density is studied analytically at high momentum p  , the coefficients of the p⁻⁴$p^{\mathrm{-4}}$ and p⁻⁶$p^{\mathrm{-6}}$ terms being tabulated for N=2–5$N=2\text{–}5$ inclusive. Their dependence on powers of N   is exhibited numerically. Finally, the functional relationship between γIB(x,y)${\gamma }_{\mathrm{IB}}(x,y)$ and γF(x,y)${\gamma }_{\mathrm{F}}(x,y)$ is formally set out and illustrated.     

Interactions of a Charged Particle with Parallel Two-Dimensional Quantum Electron Gases

By using the linearized quantum hydrodynamic (QHD) theory, electronic excitations induced by a charged particle moving between or over two parallel two-dimensional quantum electron gases (2DQEG) are investigated. The calculation shows that the influence of the quantum effects on the interaction process should be taken into account. Including the quantum statistical and quantum diffraction effects, the general expressions of the induced potential and the stopping power are obtained. Our simulation results indicate that a V-shaped oscillatory wake potential exists in the electron gases during the test charge intrusion. Meanwhile, double peaks will occur in the stopping power when the distance of two surfaces is smaller and the test charge gets closer to any one of the two sheets.     

Antiresonance of electron tunneling through a four-quantum-dot ring with two side-coupled quantum dots

Making use of the equation of motion method and Keldysh Green function technique, we obtain the current formula for a two-terminal four-quantum-dot-ring with two side-coupled quantum dots under a DC bias voltage. Antiresonance and resonance of electron tunneling is studied by numerical calculations. Only when the quantum dots in the ring has the same single electron energy level with that of the side-coupled quantum dots, i.e. and both side-coupling are turned on at the same time, the antiresonance appear exactly at ε₀.     

Wake effects and stopping power for a charged particle moving above two-dimensional quantum electron gases

Electronic excitations induced by a charged particle moving above two-dimensional electron gases are studied by means of the linearized quantum hydrodynamic (QHD) theory. In this calculation, we show that the influence of the quantum effects on the interaction process should be taken into account. The induced potential and the perturbed density of the electron gases as well as the stopping power of the particles are derived as functions of the projectile velocity, the particle position and the density function when including the quantum statistical and quantum diffraction effects. The dependence relations of the induced potential and the particle speed around the peak position at which the stopping power takes the maximum value are also discussed in this work.     

Power spectrum analysis of the average-fluctuation density separation in interacting particle systems

The power spectrum analysis using the Lomb-Scargle false alarm probability statistic shows a clear separation between the average and fluctuating parts of the state density in embedded two-body random matrix ensembles with a mean-field for both fermion and boson systems as well as in the nuclear shell model.     

Entropy in quantum ratchet for a delta-kicked model

We investigate the evolution of Shannon entropy in quantum ratchet effect for a delta-kicked model, where a particle with initial momentum zero is periodically kicked by an asymmetric potential. It is shown that the evolution of Shannon entropy of the particle can remarkably reflect whether quantum resonance emerges and gives rise to ratchet current or not. Furthermore, for different kinds of quantum resonances, low-order or high-order quantum resonances, the evolutions of the entropy are quite different.     

Thermostatistics of the multi-dimensional q-deformed fermionic Newton oscillators

The algebraic and representative properties of the multi-dimensional q-deformed fermionic Newton oscillator algebra are discussed. This algebra is covariant under the undeformed group U(n). The high- and low-temperature thermostatistical properties of a gas of the multi-dimensional q-deformed fermionic Newton oscillators are obtained.     

Note on the equivalence of different approximations in the relaxation theory

We briefly discuss relations between different variants of the second order generalized master equations (GME), in particular among different types of the Markov-Born approximation of time-convolution GME and Born approximation in time-convolutionless one. We prove that equivalence valid in the van Hove limit does not in general apply for other types of scaling. On the other hand, for other scalings one appropriate form of the interaction representation always exist that reproduces this equivalence known from the weak-coupling (van Hove) one.     

The q-deformed Bose gas: integrability and thermodynamics

We investigate the exact solution of the q-deformed one-dimensional Bose gas to derive all integrals of motion and their corresponding eigenvalues. As an application, the thermodynamics is given and compared to an effective field theory at low temperatures.     

Order disorder transitions in Ising models in transverse fields with second neighbour interactions

The (ferromagnetic) order-disorder transitions in a class of Ising models with second neighbour interaction in transverse fields is studied using the path integral method. Within the limitations of the method, the critical fields at zero temperature are estimated for different systems.     

Quantum Phase Transitions in Matrix Product States

We present a new general and much simpler scheme to construct various quantum phase transitions （Q, PTs） in spin chain systems with matrix product ground states. By use of the scheme we take into account one kind of matrix product state （MPS） OPT and provide a concrete model. We also study the properties of the concrete example and show that a kind of Q, PT appears, accompanied by the appearance of the discontinuity of the parity absent block physical observable, diverging correlation length only for the parity absent block operator, and other properties which are that the fixed point of the transition point is an isolated intermediate-coupling fixed point of renormalization flow and the entanglement entropy of a half-infinite chain is discontinuous.