Bose-Einstein Research Articles

Non-Fermi-liquid scattering rates and anomalous band dispersion in ferropnictides

Angle-resolved photoemission spectroscopy (ARPES) is used to study the band dispersion and the quasiparticle scattering rates in two ferropnictides systems. Our ARPES results show linear-in-energy dependent scattering rates which are constant in a wide range of control parameter and which depend on the orbital character of the bands. We demonstrate that the linear energy dependence gives rise to weakly dispersing band with a strong mass enhancement when the band maximum crosses the chemical potential. In the superconducting phase the related small effective Fermi energy favors a Bardeen-Cooper-Schrieffer (BCS)\,\cite{Bardeen1957}-Bose-Einstein (BE)\,\cite{Bose1924} crossover state.

Comparative analysis of electric field influence on the quantum wells with different boundary conditions: II. Thermodynamic properties.

Thermodynamic properties of the one-dimensional (1D) quantum well (QW) with miscellaneous permutations of the Dirichlet (D) and Neumann (N) boundary conditions (BCs) at its edges in the perpendicular to the surfaces electric field are calculated. For the canonical ensemble, analytical expressions involving theta functions are found for the mean energy and heat capacity for the box with no applied voltage. Pronounced maximum accompanied by the adjacent minimum of the specific heat dependence on the temperature T for the pure Neumann QW and their absence for other BCs are predicted and explained by the structure of the corresponding energy spectrum. Applied field leads to the increase of the heat capacity and formation of the new or modification of the existing extrema what is qualitatively described by the influence of the associated electric potential. A remarkable feature of the Fermi grand canonical ensemble is, at any BC combination in zero fields, a salient maximum of observed on the T axis for one particle and its absence for any other number N of corpuscles. Qualitative and quantitative explanation of this phenomenon employs the analysis of the chemical potential and its temperature dependence for different N. It is proved that critical temperature of the Bose-Einstein (BE) condensation increases with the applied voltage for any number of particles and for any BC permutation except the ND case at small intensities what is explained again by the modification by the field of the interrelated energies. It is shown that even for the temperatures smaller than the total dipole moment may become negative for the quite moderate . For either Fermi or BE system, the influence of the electric field on the heat capacity is shown to be suppressed with N growing. Different asymptotic cases of, e.g., the small and large temperatures and low and high voltages are derived analytically and explained physically. Parallels are drawn to the similar properties of the 1D harmonic oscillator, and similarities and differences between them are discussed.

Universal dynamics on the way to thermalization

It is demonstrated how a many-body system far from thermal equilibrium can exhibit universal dynamics in passing a nonthermal fixed point. As an example, the process of Bose–Einstein (BE) condensation of a dilute cold gas is considered. If the particle flux into the low-energy modes, induced, for example by a cooling quench, is sufficiently strong, the Bose gas develops a characteristic power-law single-particle spectrum , and critical slowing down in time occurs. The fixed point is shown to be marked by the creation and dilution of tangled vortex lines. Alternatively, for a weak cooling quench and particle flux, the condensation process runs quasi-adiabatically, passing by the fixed point in the far distance, and the signatures of critical scaling remain absent.

Derivation of some new distributions in statistical mechanics using maximum entropy approach

The maximum entropy principle has been earlier used to derive the Bose Einstein(B.E.), Fermi Dirac(F.D.) & Intermediate Statistics(I.S.) distribution of statistical mechanics. The central idea of these distributions is to predict the distribution of the microstates, which are the particle of the system, on the basis of the knowledge of some macroscopic data. The latter information is specified in the form of some simple moment constraints. One distribution differs from the other in the way in which the constraints are specified. In the present paper, we have derived some new distributions similar to B.E., F.D. distributions of statistical mechanics by using maximum entropy principle. Some proofs of B.E. & F.D. distributions are shown, and at the end some new results are discussed.

Gravitational Fields: Another Fortunate Manifestation of the Higgs Mechanism

The present work discusses, in a comprehensible language and simple mathematics, the origin of the gravitational physics in the light of new recent experimental observations, achieved with the help of the tightly synchronized clocks of the GPS. These observations reveal that real space, ruling the inertial motion of matter and the propagation of light, is moving round the earth and round the sun according to a Keplerian velocity field, consistent with the local main astronomical motions. This Keplerian velocity field of real space is the quintessence of the gravitational fields and appropriately induces the observed gravitational dynamics. Such real space needs not to be invented. It is well at hand in the Quantum Field Theory (QFT), underlying the Standard Elementary Particle Model (SEPM). The QFT entails the idea that space is filled up with the Higgs condensate (HC), a very powerful quantum space (QS). The HC is a Bose-Einstein (BE) condensate of the zero spin Higgs bosons. By coupling to the HC, the elementary particles get inertial mass by the Higgs mechanism, that is, get mechanical properties. This will say that the HC rules the inertial motion of matter and the propagation of light and hence is the locally ultimate reference for rest and for motion of matter and light. The present work acknowledges that, likewise the Meissner effect in superconductors develops macroscopic screening currents, forcing magnetic fields out from superconductors, the Higgs mechanism too entails a macroscopic manifestation in the form of the Keplerian velocity field of the QS round each matter body throughout the universe, consistent with the local main astronomical motions. This Keplerian velocity field screens and thrusts the matter fields out from the HC by squeezing them into a minimum of volume. It is shown that this Keplerian velocity field of the QS appropriately induces the observed gravitational dynamics on earth, in the solar system as well as the galactic gravitational dynamics without the need of dark matter. It also provides an antigravitation mechanism accelerating the expansion of the universe. It finally is shown that this spacedynamics correctly and appropriately gives origin, in terms of simple and genuine physical effects, to all the other observed effects, caused by the gravitational fields on the propagation of light and on the rate of the clocks.

A STOCHASTIC MECHANISM FOR DNA MELTING

Deoxyribonucleic acid (DNA) is a kind of nucleic acid consisting of two strands which are made up of two Watson–Crick base pairs: adenine–thymine (AT) and guanine–cytosine (GC). There are three components of the total energy. These are the inharmonic stacking interaction, hydrogen bond interaction and the kinetic energy. Morse potential is used to mimic the hydrogen bond interaction between bases on the opposite strands for the overlapping π electrons, when two neighboring bases move out of the stack. The AT pair has 2 hydrogen bonds and the GC pair has 3 of them. The π electrons obey Bose–Einstein (BE) statistics, and the overlapping of them results in quantum fluctuation. It will be shown that this can be simplified into 〈Δy(t)Δy(t)〉 = 2DqΔt type fluctuation between the base pairs. Thus, a metropolis algorithm can be developed for the total potential energy by superposing two potential energy terms as well as including the quantum fluctuation in terms of random displacement of the π electrons. So, one can calculate the melting temperature of base pairs.

Unified Quantum Statistics, Possible Violation of Pauli Exclusion Principle, Nonlinear Equations and Some Basic Problems of Entropy

We propose that Bose-Einstein (BE) and Fermi-Dirac (FD) distributions may be unified by the nonlinear quantum equation. Further, the unified quantum statistics and possible violation of Pauli exclusion principle (PEP) at high energy are researched. Third, we propose a possibility of entropy decrease due to internal interactions in some isolated systems, in particular, for quantum statistics. Fourth, we discuss a new type of soliton equation, whose solutions may describe some statistical distributions. Finally, the moderate input negative entropy flow for open systems, etc., are investigated.

Efficiency and its bounds for a quantum Einstein engine at maximum power

We study a quantum thermal engine model for which the heat transfer law is determined by Einstein's theory of radiation. The working substance of the quantum engine is assumed to be a two-level quantum system of which the constituent particles obey Maxwell-Boltzmann (MB), Fermi-Dirac (FD), or Bose-Einstein (BE) distributions, respectively, at equilibrium. The thermal efficiency and its bounds at maximum power of these models are derived and discussed in the long and short thermal contact time limits. The similarity and difference between these models are discussed. We also compare the efficiency bounds of this quantum thermal engine to those of its classical counterpart.

Two-state Bose-Hubbard model in the hard-core boson limit

Phase transition into the phase with Bose-Einstein (BE) condensate in the two-band Bose-Hubbard model with the particle hopping in the excited band only is investigated. Instability connected with such a transition (which appears at excitation energies $\delta<\lvert t_0' \rvert$, where $\lvert t_0' \rvert$ is the particle hopping parameter) is considered. The re-entrant behaviour of spinodales is revealed in the hard-core boson limit in the region of positive values of chemical potential. It is found that the order of the phase transition undergoes a change in this case and becomes the first one; the re-entrant transition into the normal phase does not take place in reality. First order phase transitions also exist at negative values of $\delta$ (under the condition $\delta>\delta_{\mathrm{crit}}\approx-0.12\lvert t_0' \rvert$). At $\mu<0$ the phase transition mostly remains to be of the second order. The behaviour of the BE-condensate order parameter is analyzed, the $(\Theta,\mu)$ and $(\lvert t_0' \rvert,\mu)$ phase diagrams are built and localizations of tricritical points are established. The conditions are found at which the separation on the normal phase and the phase with the BE condensate takes place.

Arrhenius-kinetics evidence for quantum tunneling in microbial “social” decision rates

Social-like bacteria, fungi, and protozoa communicate chemical and behavioral signals to coordinate their specializations into an ordered group of individuals capable of fitter ecological performance. Examples of microbial “social” behaviors include sporulation and dispersion, kin recognition, and nonclonal or paired reproduction. Paired reproduction by ciliates is believed to involve intra- and intermate selection through pheromone-stimulated “courting” rituals. Such social maneuvering minimizes survival-reproduction tradeoffs while sorting superior mates from inferior ones, lowering the vertical spread of deleterious genes in geographically constricted populations and possibly promoting advantageous genetic innovations. In a previous article, I reported findings that the heterotrich Spirostomum ambiguum can out-complete mating rivals in simulated social trials by learning behavioral heuristics which it then employs to store and select sets of altruistic and deceptive signaling strategies. Frequencies of strategy use typically follow Maxwell-Boltzmann (MB), Fermi-Dirac (FD), or Bose-Einstein (BE) statistical distributions. For ciliates most adept at social decision making, a brief classical MB computational phase drives signaling behavior into a later quantum BE computational phase that condenses or favors the selection of a single fittest strategy. Appearance of the network analogue of BE condensation coincides with Hebbian-like trial-and-error learning and is consistent with the idea that cells behave as heat engines, where loss of energy associated with specific cellular machinery critical for mating decisions effectively reduces the temperature of intracellular enzymes cohering into weak Fröhlich superposition. I extend these findings by showing the rates at which ciliates switch serial behavioral strategies agree with principles of chemical reactions exhibiting linear and nonlinear Arrhenius kinetics during respective classical and quantum computational phases. Nonlinear Arrhenius kinetics in ciliate decision making suggest transitions from one signaling strategy to another result from quantum tunneling in social information processing.

The significant digit law in statistical physics

The occurrence of the nonzero leftmost digit, i.e., 1 , 2 , … , 9 , of numbers from many real world sources is not uniformly distributed as one might naively expect, but instead, the nature favors smaller ones according to a logarithmic distribution, named Benford’s law. We investigate three kinds of widely used physical statistics, i.e., the Boltzmann–Gibbs (BG) distribution, the Fermi–Dirac (FD) distribution, and the Bose–Einstein (BE) distribution, and find that the BG and FD distributions both fluctuate slightly in a periodic manner around Benford’s distribution with respect to the temperature of the system, while the BE distribution conforms to it exactly whatever the temperature is. Thus Benford’s law seems to present a general pattern for physical statistics and might be even more fundamental and profound in nature. Furthermore, various elegant properties of Benford’s law, especially the mantissa distribution of data sets, are discussed.

THERMAL VACUUM RADIATION IN SPONTANEOUSLY BROKEN SECOND-QUANTIZED THEORIES ON CURVED PHASE SPACES OF CONSTANT CURVATURE

We construct second-quantized (field) theories on coset spaces of pseudo-unitary groups U(N+,N-). The existence of degenerated quantum vacua (coherent states of zero modes) leads to a breakdown of the original pseudo-unitary symmetry. The action of some spontaneously broken symmetry transformations destabilize the vacuum and make it to radiate. We study the structure of this thermal radiation for curved phase spaces of constant curvature: complex projective spaces ℂPN - 1 = SU(N)/U(N - 1) and open complex balls ℂDN - 1 = SU(1,N - 1)/U(N - 1). Positive curvature is related to generalized Fermi–Dirac (FD) statistics, whereas negative curvature is connected with generalized Bose–Einstein (BE) statistics, the standard cases being recovered for N = 2. We also make some comments on the contribution of the vacuum (dark) energy to the cosmological constant and the phenomenon of inflation.

Thermal radiation of two-dimensional Bose-Einstein gas of surface plasmons

On a heated metal surface a two-dimensional (2D) Bose-Einstein (BE) gas of surface plasmons (SPs) exists. At the edge of the surface, SP-photon conversion (SPPC) is possible. Here we present the results of a measurement of the electromagnetic radiation caused by the SPPC at the right-angular boundary of the metal surface. The data for the photon angular distribution is in good agreement with the Sommerfeld-Maluzhinets theory. The observed effects may be useful for the measurement of optical characteristics of real metals in the IR region. The proposed method is more accurate than methods based on Fresnel relations.

Bose–Einstein-like statistics of amphiphilic self-assembly

In the present paper, we formulate a statistical mechanical framework of amphiphilic self-assembly that allows a proper understanding of surfactant self-association processes on the basis of an occupation number formalism. In this model, amphiphilic molecules in solution can occupy different levels of well-defined energies corresponding to aggregates of different aggregation numbers. Due to its definition, the occupation number of a level can only take values which are proportional to the level aggregation number, thus giving rise to a modified version of Bose-Einstein statistics. In this new level-filling scheme an adequate statistical foundation of conventional micellization thermodynamics can be attained, the occupation of the different levels being controlled by the monomer chemical potential (μk 0) in the conventional manner. The implications of the new statistics on fluctuations of the number of monomers in the different aggregation levels are analyzed. Particularly, an analogy is seen to exist between the cooperative process of micellization in self-assembling clusters and Bose-Einstein (BE) momentum condensation of molecules in the energetically most favored aggregation level. Finally, micellar growth is also a matter of study in the new formalism. © 2007 Elsevier B.V. All rights reserved.

Modeling Bose-Einstein correlations via elementary emitting cells

We propose a method of numerical modeling Bose-Einstein correlations by using the notion of the elementary emitting cell (EEC). They are intermediary objects containing identical bosons and are supposed to be produced independently during the hadronization process. Only bosons in the EEC, which represents a single quantum state here, are subjected to the effects of Bose-Einstein (BE) statistics, which forces them to follow a geometrical distribution. There are no such effects between particles from different EECs. We illustrate our proposition by calculating a representative number of typical distributions and discussing their sensitivity to EECs and their characteristics.

Emission properties from dense exciton gases in diamond

AbstractA systematic study of cathodoluminescence (CL) emission arising from free exciton recombination in diamond is given. CL spectra of free exciton emission from diamond under high excitation conditions were used to characterize properties of ultradense exciton gases at quasi‐thermal equilibrium. Theoretical spectra of excitonic emission from diamond were calculated based on Bose–Einstein (BE) statistics, taking into account collision of excitons in an indirect semiconductor like diamond. The calculated spectra agreed well with the observed spectra over a wide temperature range for high‐quality homoepitaxial chemical vapor deposition diamond thin films. The analysis showed that a high density of excitons of over 1018 cm−3 could be achieved under thermodynamic quasi‐equilibrium by continuous electron beam excitation, at which BE condensation can be expected at low temperature. These results indicate that diamond is a perfect material for the generation and detection of BE condensation which is the most characteristic features of BE statistics. (© 2006 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

COOPER PAIRS AS BOSONS

Although BCS pairs of fermions are known to obey neither Bose–Einstein (BE) commutation relations nor BE statistics, we show how Cooper pairs (CPs), whether the simple original ones or the CPs recently generalized in a many-body Bethe–Salpeter approach, being clearly distinct from BCS pairs at least obey BE statistics. Hence, contrary to widespread popular belief, CPs can undergo BE condensation to account for superconductivity if charged, as well as for neutral-atom fermion superfluidity where CPs, but uncharged, are also expected to form.

The curvaton as a Bose–Einstein condensate of chiral pseudo Nambu–Goldstone bosons

Explaining cosmic inflation by the effective dynamics of an SU ( N C ) pure gauge theory of scale Λ ∼ 10 −6 M p is lacking an explanation of the (Gaussian) spatial curvature perturbations needed to seed the formation of large-scale structure after inflation. In this work it is demonstrated how fundamentally charged fermions of mass m F ∼ 10 −12 Λ , whose approximate chiral symmetry is spontaneously broken during inflation, can cure this shortcoming. The associated gas of weakly interacting pseudo Nambu–Goldstone bosons (PNGB) undergoes Bose–Einstein (BE) condensation well before the end of inflation. This causes the occurence of condensed light scalar fields effectively acting as a curvaton. Fermions may also be charged under a gauge group G with a weak coupling g. Since fermions charged under SU ( N C ) are confined after inflation the decay of Nambu–Goldstone bosons, which reside in the condensates and in the PNGB radiation generated at reheating, is mainly into fermions solely charged under G. The associated decay rate Γ is estimated using PCAC and large N C counting. PNGB decay takes place during radiation domination after cosmological scales have entered the horizon. Neglecting the effects of the spontaneous breaking of G induced by the BE condensation, it is demonstrated that the observed spectrum of spatial curvature perturbations P ξ 1 / 2 ∼ 5 × 10 −5 is compatible with g ∼ 10 −3 , a ratio r dec ∼ 10 −4 of curvaton to radiation energy at PNGB decay, and a curvaton effective equation of state p curv = − 0.9 ρ curv .

Cost of s-fold decisions in exact Maxwell–Boltzmann, Bose–Einstein and Fermi–Dirac statistics

The exact forms of the degenerate Maxwell–Boltzmann (MB), Bose–Einstein (BE) and Fermi–Dirac (FD) entropy functions, derived by Boltzmann's principle without the Stirling approximation [R.K. Niven, Physics Letters A, 342(4) (2005) 286], are further examined. Firstly, an apparent paradox in quantization effects is resolved using the Laplace–Jaynes interpretation of probability. The energy cost of learning that a system, distributed over s equiprobable states, is in one such state (an “ s-fold decision”) is then calculated for each statistic. The analysis confirms that the cost depends on one's knowledge of the number of entities N and (for BE and FD statistics) the degeneracy, extending the findings of Niven (2005).

Energetic balance of the superconducting transition across the BCS—Bose Einstein crossover in the attractive Hubbard model

We investigate by means of Dynamical mean-field theory the crossover from BCS superconductivity to Bose-Einstein (BE) condensation of preformed pairs which occurs in the attractive Hubbard model by increasing the attraction strength. Fixing the density to a generic value $n=0.75$, we follow the evolution of the two energy scales underlying the superconducting phenomenon, the gap ${\ensuremath{\Delta}}_{0}$, and the superfluid stiffness ${D}_{S}$, which controls the phase coherence. The BCS--BE crossover is clearly mirrored in a change in the hierarchy of these two scales, the smallest of the two controlling the critical temperature. In the whole intermediate-to-strong-coupling region ${T}_{c}$ scales with ${D}_{S}$, while ${T}_{C}$ is proportional to ${\ensuremath{\Delta}}_{0}$ only in the BCS regime. This evolution as a function of the interaction qualitatively resembles what happens in the cuprates when the doping is decreased towards the Mott insulator. This continuous change reflects also in the energetic balance at the superconducting transition. While, as it is well known, superconductivity is stabilized by a potential energy gain in the BCS regime, the strong-coupling superconductivity is made stable by a reduction of kinetic energy. Interestingly the intermediate-coupling region, where the maximum ${T}_{c}$ is achieved, behaves similarly to the strong-coupling regime, and its gain in kinetic energy is the largest as a function of the coupling. Since the integral of the optical conductivity is proportional to the kinetic energy, the above finding implies that the attractive Hubbard model can account qualitatively for the anomalous behavior of optical spectra around ${T}_{c}$, where an increase of spectral weight is observed in under and optimally doped cuprates, while the overdoped samples have a more standard behavior. This qualitative agreement is lost in the normal phase, specifically at strong coupling, calling for the inclusion of strong correlation effects in the theoretical description.