Yong-li Ma

Efficiency at maximum power of a quantum Otto cycle within finite-time or irreversible thermodynamics.

We consider the efficiency at maximum power of a quantum Otto engine, which uses a spin or a harmonic system as its working substance and works between two heat reservoirs at constant temperatures T(h) and T(c) (<T(h)). Although the behavior of spin-1/2 system differs substantially from that of the harmonic system in that they obey two typical quantum statistics, the efficiencies at maximum power based on these two different kinds of quantum systems are bounded from the upper side by the same expression η(mp)≤η(+)≡η(C)(2)/[η(C)-(1-η(C))ln(1-η(C))] with η(C)=1-T(c)/T(h) as the Carnot efficiency. This expression η(mp) possesses the same universality of the CA efficiency η(CA)=1-√(1-η(C)) at small relative temperature difference. Within the context of irreversible thermodynamics, we calculate the Onsager coefficients and show that the value of η(CA) is indeed the upper bound of EMP for an Otto engine working in the linear-response regime.

Quantum-mechanical engines working with an ideal gas with a finite number of particles confined in a power-law trap

Based on quantum thermodynamic processes, we make a quantum-mechanical (QM) extension of the typical heat engine cycles, such as the Carnot, Brayton, Otto, Diesel cycles, etc., with no introduction of the concept of temperature. When these QM engine cycles are implemented by an ideal gas confined in an arbitrary power-law trap, a relation between the quantum adiabatic exponent and trap exponent is found. The differences and similarities between the efficiency of a given QM engine cycle and its classical counterpart are revealed and discussed.

Coefficient of performance under maximum χ criterion in a two-level atomic system as a refrigerator.

A two-level atomic system as a working substance is used to set up a refrigerator consisting of two quantum adiabatic and two isochoric processes (two constant-frequency processes ω_{a} and ω_{b} with ω_{a}<ω_{b}), during which the two-level system is in contact with two heat reservoirs at temperatures T_{h} and T_{c}(<T_{h}). Considering finite-time operation of two isochoric processes, we derive analytical expressions for cooling rate R and coefficient of performance (COP) ɛ. The COP at maximum χ(=ɛR) figure of merit is numerically determined, and it is proved to be in nice agreement with the so-called Curzon and Ahlborn COP ɛ_{CA}=sqrt[1+ɛ_{C}]-1, where ɛ_{C}=T_{c}/(T_{h}-T_{c}) is the Carnot COP. In the high-temperature limit, the COP at maximum χ figure of merit, ɛ^{*}, can be expressed analytically by ɛ^{*}=ɛ_{+}≡(sqrt[9+8ɛ_{C}]-3)/2, which was derived previously as the upper bound of optimal COP for the low-dissipation or minimally nonlinear irreversible refrigerators. Within the context of irreversible thermodynamics, we prove that the value of ɛ_{+} is also the upper bound of COP at maximum χ figure of merit when we regard our model as a linear irreversible refrigerator.

Resonant Interactions of Collective Modes in a Quasi-One-Dimensional Attractive Bose–Einstein Condensate

The resonant interaction between collective modes in a quasi-one-dimensional (Q1D) attractive Bose–Einstein condensate (BEC) is considered. Nonlinearly coupled amplitude equations are derived using a method of multiple scales. Coupling matrix elements describing mode–mode resonances in both Landau and Beliaev mechanisms are calculated analytically. In particular, second-harmonic generation and three-mode resonant interaction of the collective modes in Q1D BEC are investigated in detail. The result shows that the physics of the resonant mode couplings in attractive Q1D BEC is richer than that of repulsive Q1D BEC.

A New Approach for the Statistical Thermodynamic Theory of the Nonextensive Systems Confined in Different Finite Traps

For a small system at a low temperature, thermal fluctuation and quantum effect play important roles in quantum thermodynamics. Starting from micro-canonical ensemble, we generalize the Boltzmann–Gibbs statistical factor from infinite to finite systems, no matter the interactions between particles are considered or not. This generalized factor, similar to Tsallis’s q-form as a power-law distribution, has the restriction of finite energy spectrum and includes the nonextensivities of the small systems. We derive the exact expression for distribution of average particle numbers in the interacting classical and quantum nonextensive systems within a generalized canonical ensemble. This expression in the almost independent or elementary excitation quantum finite systems is similar to the corresponding ones obtained from the conventional grand-canonical ensemble. In the reconstruction for the statistical theory of the small systems, we present the entropy of the equilibrium systems and equation of total thermal ...

Nuclear-fusion enhancement in condensed matter with impacting and screening

A theoretical study of the nuclear fusion in condensed matter is reported. We present a simple model for the fusion with two effects, impacting and screening, characterized by impacting factor Q and screening length λ, respectively. Explicit expressions and results are given for the fusion rate R(E0/Q, λ), where E0 is the incident energy. R is enhanced by the cooperation of the two effects. Calculated fusion yields and/or rates are, respectively, in reasonable agreement with the experimental data obtained in cluster-impact fusion and deuterium-implanted titanium fusion. Predicted cold-fusion rates are still lower than the one observed experimentally, except on extremely high density of deuteron atoms and strongly coherent collisions in solids.

Vortices pinned by random columnar defects in a global phase diagram

Abstract Based on the Bose/vortex-glass theory, the property of vortices pinned by random columnar defects is investigated in a global phase diagram. The renormalized pinning energy is determined by thermal fluctuation as well as by the statistical origin of the random columnar defects. The thermal renormalized factor is determined by solving a two-dimensional Schrodinger equation with the potential well. With the use of the pinning energy obtained, the temperature-dependent accommodation field line and the field-dependent temperature lines of crossover, depinning and delocalization are estimated quantitatively in a self-consistent manner. The expressions for the critical current density, the current-dependent activation energy and its exponent are deduced in various pinning regimes. The results show that the creep rates agree well with the experiments in a very wide range of the phase diagrams, reflecting a rich and varied vortex picture below the accommodation field line and a monotonic vortex behavior above the accommodation field line.

Commensurate vortex lattices pinned by a periodic lattice of columnar defects

The effects of a periodic hexagonal lattice of columnar defects on the curves of magnetic induction B (H ), vortex-lattice melting Tm (H ) and critical current density Jc (H ) versus external field H are investigated, including the effects of vortex interaction, thermal and quantum fluctuations, an applied current drive and columnar pin disorder. It is found theoretically that the smallest slope of B (H ) occurs when the magnetic induction B matches the regular pinning field npin 0 over a finite range of H . This commensuration leads to an inhibition of the vortex-lattice melting and a large enhancement of the critical current density, i.e., the curves of Tm (H ) and Jc (H ) each have a series of broad plateaus. The applied current drive, electric field-like in form, shifts this melting curve downwards. Jc (T ) is the power-3/2 temperature decay at intermediate temperatures and decays exponentially to zero at high temperatures. The pin disorder and ion straggling reduce these favourable effects and wash out the plateaus when they become equal to certain critical values.

Corrected Sum Rule, Generalized Virial Identity and Elementary Excitation Spectrum of Bose-Einstein Condensates at any Trapped Atom Number

Using a corrected sum rule and a generalized virial identity, we study the analytical expression for entire modes of the collective elementary excitation spectrum in a trapped Bose–Einstein condensate at any atom number. Explicit analytical formulas for the spectrum are obtained for the harmonic traps with both spherical symmetry and axial symmetry using the gaussian approximation for the N-body ground-state wave function of the condensate. These formulas give the simple dependence of all energy levels on the atom numbers, their interaction strength and trap geometry parameters.

The frequency response of large-amplitude oscillations of a trapped Bose condensed gas

We study the frequency response of large-amplitude oscillations of a trapped Bose condensed gas. On the basis of the Thomas?Fermi approximation, we deduce the hydrodynamical equation including the excitation source of the velocity drive, and obtain the analytical expression for the frequency as a function of velocity fluctuation amplitude, trap geometry, and symmetry of modes. By solving the expansion equation after switching off the trap, we find a simple relationship between the velocity amplitude and the oscillation amplitude. The theoretical calculations on the response frequencies agree well with the existing experimental observations.