Bose-Einstein Research Articles

Photon propagation in a charged Bose–Einstein condensate model

We consider the propagation of photons in a model of a charged scalar Bose-Einstein (BE) condensate. We determine the dispersion relations of the collective modes, as well as the photon polarization tensor and the dielectric constant in the model. Two modes correspond to the transverse photon polarizations, with dispersion relations of the usual form for transverse photons in a plasma. The other two modes, denoted as the (±)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\pm )$$\\end{document} modes, are combinations of the longitudinal photon and the massive scalar field. Their dispersion relations behave very differently as functions of momentum. The (+)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(+)$$\\end{document} mode dispersion relation increases steadily and remains greater than the momentum as the momentum increases. The dispersion relation of the (-)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(-)$$\\end{document} mode decreases in a given momentum range, with the group velocity being negative in that range, while in another range it increases steadily but remains smaller than the momentum, akin to the situation in a medium with an index of refraction greater than 1. We consider the non-relativistic limit of the (±)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\pm )$$\\end{document} dispersion relations and discuss some aspects of the results. We also determine the wavefunctions of the (±)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\pm )$$\\end{document} modes, which are useful to obtain the corrections to the dispersion relations, e.g., imaginary parts due to the damping effects and/or the effects of scattering, due to the interactions with the excitations of the system. The results can be useful in various physical contexts that have been considered in the literature involving the electrodynamics of a charged scalar BE condensate.

Development of a High Min-Entropy Quantum Random Number Generator Based on Amplified Spontaneous Emission.

We present the theory, architecture, and performance characteristics of a quantum random number generator (QRNG) which operates in a PCI express form factor-compatible plug-and-play design. The QRNG relies on a thermal light source (in this case, amplified spontaneous emission), which exhibits photon bunching according to the Bose-Einstein (BE) statistics. We demonstrate that 98.7% of the unprocessed random bit stream min-entropy is traceable to the BE (quantum) signal. The classical component is then removed using a non-reuse shift-XOR protocol, and the final random numbers are generated at a 200 Mbps rate and shown to pass the statistical randomness test suites FIPS 140-2, Alphabit, SmallCrush, DIEHARD, and Rabbit of the TestU01 library.

Information geometry and Bose-Einstein condensation.

It is a long held conjecture in the connection between information geometry (IG) and thermodynamics that the curvature endowed by IG diverges at phase transitions. Recent work on the IG of Bose-Einstein (BE) gases challenged this conjecture by saying that in the limit of fugacity approaching unit-where BE condensation is expected-the curvature does not diverge; rather, it converges to zero. However, as the discontinuous behavior that identifies condensation is only observed at the thermodynamic limit, a study of the IG curvature at a finite number of particles, N, is in order from which the thermodynamic behavior can be observed by taking the thermodynamic limit ( N→∞) posteriorly. This article presents such a study. We find that for a trapped gas, as N increases, the values of curvature decrease proportionally to a power of N, while the temperature at which the maximum value of curvature occurs approaches the usually defined critical temperature. This means that, in the thermodynamic limit, the curvature has a limited value where a phase transition is observed, contradicting the forementioned conjecture.

Dynamical analysis of higher-order localized waves for a three-component coupled nonlinear Schrödinger equation

This paper examines the three-component coupled nonlinear Schrödinger equation, which has various applications in deep ocean, nonlinear optics, Bose–Einstein (BE) condensates, and more. On the basis of seed solutions and a Lax pair, the Nth-order iterative expressions for the solutions are derived by using the generalized Darboux transformation. The evolution plots of dark-bright-rogue wave or breather-rogue wave are then obtained via numerical simulation. Particularly, a novel rogue wave propagation trajectory is found in the second and third order localized wave solutions. Moreover, by increasing the value of the free parameter α and β, the nonlinear waves merge with each other distinctly. The results further reveal the abundant dynamical patterns of localized waves in the three-component coupled system.

Spinor Bose-Einstein condensates

Bose-Einstein (BE) condensation is a phenomenon in which a macroscopic number of particles occupy a single-particle state. Once a system undergoes BE condensation, a significant fraction of particles behave in lockstep, leading to a number of spectacular macroscopic quantum phenomena. This article delineates fundamental aspects of BE condensates with an emphasis on spin degrees of freedom. Here the gauge and spin degrees of freedom are coupled to produce a rich variety of spinor superfluidity and topological excitations.

Bose-Einstein statistics for a finite number of particles

This article presents a study of the grand canonical Bose-Einstein (BE) statistics for a finite number of particles in an arbitrary quantum system. The thermodynamical quantities that identify BE condensation -- namely, the fraction of particles in the ground state and the specific heat -- are calculated here exactly in terms of temperature and fugacity. These calculations are complemented by a numerical calculation of fugacity in terms of the number of particles, without taking the thermodynamic limit. The main advantage of this approach is that it does not rely on approximations made in the vicinity of the usually defined critical temperature, rather it makes calculations with arbitrary precision possible, irrespective of temperature. Graphs for the calculated thermodynamical quantities are presented in comparison to the results previously obtained in the thermodynamic limit. In particular, it is observed that for the gas trapped in a 3-dimensional box the derivative of specific heat reaches smaller values than what was expected in the thermodynamic limit -- here, this result is also verified with analytical calculations. This is an important result for understanding the role of the thermodynamic limit in phase transitions and makes possible to further study BE statistics without relying neither on the thermodynamic limit nor on approximations near critical temperature.

Bose-Einstein Condensation of Cooper-Pairs in the Conventional Superconductors

Observed crossover events between different power functions of absolute temperature occurring below about ~1 K in the temperature dependence of the heat capacity or the thermal conductivity of the conventional superconductors are identified as transitions from Maxwell-Boltzmann to Bose-Einstein (BE) statistics of the Cooper-pairs. Because of the low mass of the Cooper pairs of 2me (with me as mass of the electron) and their high density, the BE-condensation temperature, TBE, of the Cooper-pairs is about five orders of magnitude higher than for the dilute alkali atom condensates. The condensation temperature TBE turns out to be proportional to the superconducting transition temperature TSC. From the observed TBE-values it is possible to calculate the density of the Cooper pairs. Assuming that the Cooper pairs form a dense gas of bosons, the diameter of the Cooper-pair orbitals turns out to be equal to the London penetration depth. As a conclusion, due to the large orbital diamagnetism of the Cooper-pairs pairs, only one layer of Cooper-pairs, next to the inner surface of the sample, is sufficient to shield an applied external magnetic field completely.

Relativistic freeze-in with scalar dark matter in a gauged B \u2212 L model and electroweak symmetry breaking

We explore relativistic freeze-in production of scalar dark matter in gauged B − L model, where we focus on the production of dark matter from the decay and annihilation of Standard Model (SM) and B − L Higgs bosons. We consider the Bose-Einstein (BE) and Fermi-Dirac (FD) statistics, along with the thermal mass correction of the SM Higgs boson in our analysis. We show that in addition to the SM Higgs boson, the annihilation and decay of the B − L scalar can also contribute substantially to the dark matter relic density. Potential effects of electroweak symmetry breaking (EWSB) and thermal mass correction in BE framework enhance the dark matter relic substantially as it freezes-in near EWSB temperature via scalar annihilation. However, such effects are not so prominent when the dark matter freezes-in at a later epoch than EWSB, dominantly by decay of scalars. The results of this analysis are rather generic, and applicable to other similar scenarios.

A study on Raga characterization in Indian classical music in the light of MB and BE distribution

Raga characterization in Indian classical music is an important aspect of music learning in this country. But the methods usually followed are mostly qualitative. In this study, we intend to quantify such abstractness using measurable parameters. To study musical information congregation quantifiably, we introduce methods based on well-known concepts used in Statistical Physics, namely Maxwell-Boltzmann (MB) and Bose-Einstein (BE) distribution. In this present study, these distributions have been applied on the chosen acoustic signals to find new parameters (equivalent to ‘temperature’ in physical systems) which can distinguish between different features of different ragas (containing the same notes) in Indian classical music. Music clips chosen were the ‘Alap’ part of these three different ragas (Marwa, Puriya, Sohini) sung by a legendary classical music maestro. All of the chosen three ragas are based on the following same note structure: Sa, komal Re, shuddh Ga, tivra Ma, shuddh Dha, shuddh Ni. To apply MB statistics to music, it is assumed that different notes with different occurrence frequencies are at different energy levels, the distribution of which follows the MB distribution pattern. In case of BE statistics, a rank-frequency distribution of the time durations of various notes of different ragas is studied. The resulting analysis gives rise to a number of parameters that help to categorize the individual characteristics of ragas. The methods studied here are novel in the music research field and can prove to be useful in the fields of music and speech as quantifying parameters for style identification.

Predicting COVID-19 confirmed cases in New York and DKI Jakarta by nonlinear fitting of a Bose–Einstein energy distribution and its implications on social restrictions

ObjectiveGlobal society pays huge economic toll and live loss due to COVID-19 (Coronavirus Disease 2019) pandemic. In order to have a better management of this pandemic, many institutions develop their own models to predict number of COVID-19 cases, hospitalizations and mortalities. These models, however, are shown to be unreliable and need to be revised on a daily basis. MethodsHere, we develop a Bose–Einstein (BE)-based statistical model to predict daily COVID-19 cases up to 14 days in advance. This fat-tailed model is chosen based on three reasons. First, it contains a peak and decaying phase. Second, it also has both accelerated and decelerated phases which are similarly observed in an epidemic curve. Third, the shape of both the BE energy distribution and the epidemic curve is controlled by a set of parameters. The BE model daily predictions are then verified against simulated data and confirmed COVID-19 daily cases from two epidemic centres, i.e. New York and DKI Jakarta. ResultOver- predictions occur at the earlier stage of the epidemic for all data sets. Models parameters for both simulated and New York data converge to a certain value only at the latest stage of the epidemic progress. At this stage, model's skill is high for both simulated and New York data, i.e. the predictability is greater than 80% with decreasing RMSE. On the other hand, at that stage, the DKI's model's predictability is still fluctuating with increasing RMSE. ConclusionThis implies that New York could leave the stay-at-home order, but DKI Jakarta should continue its large-scale social restriction order. There remains a great challenge in predicting the full course of an epidemic using small data collected during the earlier phase of the epidemic.

Quantum Vacuum: The Structure of Empty Space–Time and Quintessence with Gauge Symmetry Group SU(2) ⊗ U(1)

We consider the formation of structured and massless particles with spin 1, by using the Yang–Mills-like stochastic equations system for the group symmetry S U ( 2 ) ⊗ U ( 1 ) without taking into account the nonlinear term characterizing self-action. We prove that, in the first phase of relaxation, as a result of multi-scale random fluctuations of quantum fields, massless particles with spin 1, further referred as hions, are generated in the form of statistically stable quantized structures, which are localized on 2D topological manifolds. We also study the wave state and the geometrical structure of the hion when as a free particle and, accordingly, while it interacts with a random environment becoming a quasi-particle with a finite lifetime. In the second phase of relaxation, the vector boson makes spontaneous transitions to other massless and mass states. The problem of entanglement of two hions with opposite projections of the spins + 1 and − 1 and the formation of a scalar zero-spin boson are also thoroughly studied. We analyze the properties of the scalar field and show that it corresponds to the Bose–Einstein (BE) condensate. The scalar boson decay problems, as well as a number of features characterizing the stability of BE condensate, are also discussed. Then, we report on the structure of empty space–time in the context of new properties of the quantum vacuum, implying on the existence of a natural quantum computer with complicated logic, which manifests in the form of dark energy. The possibilities of space–time engineering are also discussed.

Hartree–Fock analysis of the effects of long-range interactions on the Bose–Einstein condensation

We consider a Bose gas with two-body Kac-like scaled interactions where is a given repulsive and integrable potential, while is a positive parameter which controls the range of the interactions and their amplitude at a distance r. Using the Hartree–Fock (HF) approximation we find that, at finite non-zero temperatures, the Bose–Einstein (BE) condensation is destroyed by the repulsive interactions when they are sufficiently long-range. More precisely, we show that for sufficiently small but finite the off-diagonal part of the one-body density matrix always vanishes at large distances. Our analysis sheds light on the coupling between critical correlations and long-range interactions, which might lead to the breakdown of the off-diagonal long-range order even beyond the HF approximation. Furthermore, our HF analysis shows the existence of a threshold value above which the BE condensation is restored. Since is an unbounded increasing function of the temperature this implies for a fixed , namely for a fixed scaled potential, that a condensate cannot form above some critical temperature whatever the value of the density.

RETRACTED: Bose-Einstein (B-E) photon energy reformation for cooling and heating the premises naturally

Abstract Conventional heating and cooling systems consume fossil fuels and release toxic gases into the environment, so sustainable heating and cooling systems are urgently needed. To mitigate this perplexity, photon particles are being decoded by the Bose–Einstein ( B-E ) photon distribution mechanism in the Helium assisted glazing wall to cool the building naturally by inducing photonic band-gap of cooling state photons. This cooling-state photon denoted, as the Hossain Cooling Photon ( HcP − ). Once need this HcP − can be transformed into a thermal state photon, denoted as the Hossain Thermal Photon ( HtP − ) formed by Higgs Bosons ( H → γγ − ) electromagnetic quantum field utilizing by two diode thermal semiconductor. Because the H → γγ − quantum field is initiated by an extremely short-range weak force that enforces the electrically charged HcP − quantum get excited to transform it into an HtP − . The formation of HcP − and the transformation of HtP − are being demonstrated by a series of mathematical tests that confirms the viability of the decoded photons ( HcP − and HtP − ) are actively feasible into the glazing wall to cool and heat the premises naturally.

RETRACTED: Photonic thermal control to naturally cool and heat the building

Abstract Photon particle has been modeled to be decoded by the curtain wall of the building to create a natural cooling and heating system for a building by implementing the Bose-Einstein (B-E) photon distribution mechanism into Helium assisted building curtain wall where the photonic band gap state photon will be locally induced to cool the building naturally by the cooling state of the photons. This cooling state photon, denominated as Hossain Cooling Photon (HcP−). Once needed, this (HcP−) can be transformed into thermal state photon by implementing the quantum Higgs Boson BR(H → γγ−) to create the electromagnetic field (EmF) using two diode thermal semiconductors. Just because Higgs boson BR (H → γγ) quantum field has extremely short range of weak force that initiates Higgs Boson BR (H → γγ) quantum get excited. Therefore, electrically charged cooling state photon (HcP−) will be transformed into a thermal stage photon, referred to here as the Hossain Thermal Photon (HtP−). To confirm this HcP− formation and transformation it into HtP−, a series of mathematical tests has been performed which revealed that formation and transformation of HcP− and HtP− are indeed doable to decode the photons into the curtain wall to cool and heat the building naturally.

An analytic relation between the fractional parameter in the Mittag–Leffler function and the chemical potential in the Bose–Einstein distribution through the analysis of the NASA COBE monopole data

To extend the Bose-Einstein (BE) distribution to fractional order, we turn our attention to the differential equation, df/dx = −f − f2. It is satisfied with the stationary solution, f(x) = 1/(ex + μ − 1), of the Kompaneets equation, where μ is the constant chemical potential. Setting R = 1/f, we obtain a linear differential equation for R. Then, the Caputo fractional derivative of order p (p > 0) is introduced in place of the derivative of x, and fractional BE distribution is obtained, where function ex is replaced by the Mittag–Leffler (ML) function Ep(xp). Using the integral representation of the ML function, we obtain a new formula. Based on the analysis of the NASA COBE monopole data, an identity p ≃ e−μ is found.

Thermalization of one-dimensional photon gas and thermal lasers in erbium-doped fibers.

We demonstrate thermalization and Bose-Einstein (BE) distribution of photons in standard erbium-doped fibers (edf) in a broad spectral range up to ~200nm at the 1550nm wavelength regime. Our measurements were done at a room temperature ~300K and 77K. It is a special demonstration of thermalization of photons in fiber cavities and even in open fibers. They are one-dimensional (1D), meters-long, with low finesse, high loss and small capture fraction of the spontaneous emission. Moreover, we find in the edf cavities coexistence of thermal-equilibrium (TE) and thermal lasing without an overall inversion (T-LWI). The experimental results are supported by a theoretical analysis based on the rate equations.

A realistic analysis of the phonon growth characteristics in a degenerate semiconductor using a simplified model of Fermi-Dirac distribution

The phonon growth characteristic in a degenerate semiconductor has been calculated under the condition of low temperature. If the lattice temperature is high, the energy of the intravalley acoustic phonon is negligibly small compared to the average thermal energy of the electrons. Hence one can traditionally assume the electron-phonon collisions to be elastic and approximate the Bose-Einstein (B.E.) distribution for the phonons by the simple equipartition law. However, in the present analysis at the low lattice temperatures, the interaction of the non equilibrium electrons with the acoustic phonons becomes inelastic and the simple equipartition law for the phonon distribution is not valid. Hence the analysis is made taking into account the inelastic collisions and the complete form of the B.E. distribution. The high-field distribution function of the carriers given by Fermi-Dirac (F.D.) function at the field dependent carrier temperature, has been approximated by a well tested model that apparently overcomes the intrinsic problem of correct evaluation of the integrals involving the product and powers of the Fermi function. Hence the results thus obtained are more reliable compared to the rough estimation that one may obtain from using the exact F.D. function, but taking recourse to some over simplified approximations.

DISTRIBUTION OF PARASTATISTICS FUNCTIONS: AN OVERVIEW OF THERMODYNAMICS PROPERTIES

This study aims to determine the thermodynamic properties of the parastatistics system of order two. The thermodynamic properties to be searched include the Grand Canonical Partition Function (GCPF) Z, and the average number of particles N. These parastatistics systems is in a more general form compared to quantum statistical distribution that has been known previously, i.e.: the Fermi-Dirac (FD) and Bose-Einstein (BE). Starting from the recursion relation of grand canonical partition function for parastatistics system of order two that has been known, recuresion linkages for some simple thermodynamic functions for parastatistics system of order two are derived. The recursion linkages are then used to calculate the thermodynamic functions of the model system of identical particles with limited energy levels which is similar to the harmonic oscillator. From these results we concluded that from the Grand Canonical Partition Function (GCPF), Z, the thermodynamics properties of parastatistics system of order two (paraboson and parafermion) can be derived and have similar shape with parastatistics system of order one (Boson and Fermion). The similarity of the graph shows similar thermodynamic properties. Keywords: parastatistics, thermodynamic properties

Fermi-Dirac and Bose-Einstein Integrals and Their Applications to Resistivity in Some Magnetic Alloys, Part III

The Fermi-Dirac (FD) and Bose-Einstein (BE) integrals were applied to a quantum system to estimate the density of particles and relaxation time in some magnetic alloys at low temperatures. An integral part in the energy equations of vibrations (phonons), spin waves (magnons), and electrons was mathematically treated. Comparison between theoretical and experimental results gave good semi-empirical relations and some physical constants.

Statistics of neutrinos and relativistic effective degrees of freedom in the early universe

Abstract We study the effects of the presence of non-pure fermionic neutrinos on the relativistic effective degrees of freedom g ∗ in the early universe. The statistics of neutrinos is transformed from Fermi–Dirac (FD) to Bose–Einstein (BE) via Maxwell–Boltzmann (MB) statistics. The equilibrium energy density of pure bosonic neutrinos is larger than the energy density of pure fermionic neutrinos. One may expect that the relation g ∗ FD g ∗ MB g ∗ BE . We show that this relation is not always satisfied with degenerate neutrinos. We discuss briefly the cosmological consequences of this transformation for dark matter problem as well as the baryon–photon ratio in the universe.