Narrow Results

We present an inequality that gives a lower bound on the expectation value of certain two-body interaction potentials in a general state on Fock space in terms of the corresponding expectation value for thermal equilibrium states of non-interacting systems and the difference in the free energy. This bound can be viewed as a rigorous version of first-order perturbation theory for many-body systems at positive temperature. As an application, we give a proof of the first two terms in a high density (and high temperature) expansion of the free energy of jellium with Coulomb interactions, both in the fermionic and bosonic case. For bosons, our method works above the transition temperature (for the non-interacting gas) for Bose–Einstein condensation.

We consider Bose–Einstein condensation (BEC) on graphs with transient adjacency matrix. We prove the equivalence of BEC and non-factoriality of the quasi-free state. Moreover, quasi-free states exhibiting BEC decompose into generalized coherent states. We review necessary and sufficient conditions that a quasi-free state is faithful, factor, and pure and quasi-free states are quasi-equivalent, including the papers of Araki and Shiraishi [1], Araki [2], and Araki and Yamagami [3]. Using their formats and results, we prove necessary and sufficient conditions that a generalized coherent state is faithful, factor, and pure and generalized coherent states are quasi-equivalent as well.

We consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number $N$ becomes large. In the dilute regime, when the interaction potentials have the length scale of order $O(N^{-1})$, we show that the leading order of the ground state energy is captured correctly by the Gross–Pitaevskii energy functional and that the many-body ground state fully condensates on the Gross–Pitaevskii minimizers. In the mean-field regime, when the interaction length scale is $O(1)$, we are able to verify Bogoliubov’s approximation and obtain the second order expansion of the ground state energy. While such asymptotic results have several precursors in the literature on one-component condensates, the adaptation to the multi-component setting is non-trivial in various respects and the analysis will be presented in detail.

We consider a 3D quantum system of $N$ identical bosons in a trapping potential $|x{|}^p$, with $p\ge 0$, interacting via a Newton potential with an attractive interaction strength $a_N$. For a fixed large $N$ and the coupling constant $a_N$ smaller than a critical value $a_{\ast }$ (Chandrasekhar limit mass), in an appropriate sense, the many-body system admits a ground state. We investigate the blow-up behavior of the ground state energy as well as the ground states when $a_N$ approaches $a_{\ast }$ sufficiently slowly in the limit $N\to \infty$. The blow-up profile is given by the Gagliardo–Nirenberg solutions.

We consider a gas of interacting bosons trapped in a box of side length one in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s prediction for the ground state energy and the low-energy excitation spectrum. This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein.

Optical computing devices can be implemented based on controlled generation of soliton trains in single and multicomponent Bose–Einstein condensates (BEC). Our concepts utilize the phenomenon that the frequency of soliton trains in BEC can be governed by changing interactions within the atom cloud [F. Pinsker, N. G. Berloff and V. M. Pérez-García, Phys. Rev. A87, 053624 (2013), arXiv:1305.4097]. We use this property to store numbers in terms of those frequencies for a short time until observation. The properties of soliton trains can be changed in an intended way by other components of BEC occupying comparable states or via phase engineering. We elucidate, in which sense, such an additional degree of freedom can be regarded as a tool for controlled manipulation of data. Finally, the outcome of any manipulation made is read out by observing the signature within the density profile.

Quantum condensates in nuclear matter are treated beyond the mean-field approximation, with the inclusion of cluster formation. The occurrence of a separate binding pole in the four-particle propagator in nuclear matter is investigated with respect to the formation of a condensate of α-like particles (quartetting), which is dependent on temperature and density. Due to Pauli blocking, the formation of an α-like condensate is limited to the low-density region. Consequences for finite nuclei are considered. In particular, excitations of self-conjugate 2n-Z–2n-N nuclei near the n-α-breakup threshold are candidates for quartetting. We review some results and discuss their consequences. Exploratory calculations are performed for the density dependence of the α condensate fraction at zero temperature to address the suppression of the four-particle condensate below nuclear-matter density.

The universal character of non-relativistic large three-body bosonic systems is addressed, with focus on highly interesting situations that occur in low-energy nuclear and atomic physics. Investigations on the trajectory of the first excited Efimov state, in a renormalized zero-range three-body model for a system with two bound and one virtual two-body subsystems, are reported. The approach is applied to n-n-¹⁸C, where the n - n virtual energy and the three-body ground state are kept fixed. It is shown that the real part of the elastic s-wave phase-shift () presents a zero, or a pole in , when the system has an Efimov excited or virtual state. A brief discussion is given on the relevance of the approach for ultracold atom physics with tunable scattering lengths.

The behavior of a Bose–Einstein condensate in a homogeneous gravitational field is analyzed. We consider two different trapping potentials. Firstly, the gas is inside a finite container. The effects of the finiteness of the height of the container in connection with the presence of a homogeneous gravitational field are mathematically analyzed and the resulting energy eigenvalues are deduced and used to obtain the corresponding partition function and ensuing thermodynamical properties. Secondly, the trapping potential is an anisotropic harmonic oscillator and the effects of the gravitational field and of the zero-point energy on the condensation temperature are also considered. These results are employed in order to put forward an experiment which could test the so-called Einstein Equivalence Principle.

We have studied the effects of Lorentz-violation in the Bose–Einstein condensation (BEC) of an ideal boson gas, by assessing both the nonrelativistic and ultrarelativistic limits. Our model describes a massive complex scalar field coupled to a CPT-even and Lorentz-violating background. We first analyze the nonrelativistic case, at this level by using experimental data, we obtain upper-bounds for some LIV parameters. In the sequel, we have constructed the partition function for the relativistic ideal boson gas which to be able of a consistent description requires the imposition of severe restrictions on some LIV coefficients. In both cases, we have demonstrated that the LIV contributions are contained in an overall factor, which multiplies almost all thermodynamical properties. An exception is the fraction of the condensed particles.

In this paper, the advantages of pion versus kaon interferometry as a measure to probe the degree of source coherence are studied by a expanding boson gas model with a harmonic oscillator potential. We investigate the conditions about occurrence of Bose–Einstein condensation and analyze its impacts on the chaotic parameter λ. The results indicate that this finite condensation for pion system decreases the value of λ, but influence slightly for kaon system.

We investigate Bose-Einstein condensation of a gas of non-interacting Bose particles moving in the background of a periodic lattice of delta functions. In the one-dimensional case, where one has no condensation in the free case, we showed that this property persist also in the presence of the lattice. In addition we formulated some conditions on the spectral functions which would allow for condensation.

A Bose–Einstein condensation theory for any integer spin using noncommutative quantum mechanics methods is considered. The effective potential is derived as a multipolar expansion in the non-commutativity parameter $(𝜃)$ and, at second order in $𝜃$, our procedure yields to the standard dipole–dipole interaction with ${𝜃}^2$ playing the role of the strength interaction parameter. The generalized Gross–Pitaevskii equation containing nonlocal dipolar contributions is found. For ${}^{52}\mathrm{\text{Cr}}$ isotopes $𝜃=C_{dd}/4\pi$ becomes $\sim$$10^{-11}\mathrm{\text{cm}}$ and, thus for this value of $𝜃$ one cannot distinguish interactions coming from non-commutativity or those of dynamical origin.

The hypothesis of an 'invisible' axion was made by Misha Shifman and others, approximately thirty years ago. It has turned out to be an unusually fruitful idea, crossing boundaries between particle physics, astrophysics and cosmology. An axion with mass of order 10^-5 eV (with large uncertainties) is one of the leading candidates for the dark matter of the universe. It was found recently that dark matter axions thermalize and form a Bose-Einstein condensate (BEC). Because they form a BEC, axions differ from ordinary cold dark matter (CDM) in the non-linear regime of structure formation and upon entering the horizon. Axion BEC provides a mechanism for the production of net overall rotation in dark matter halos, and for the alignment of cosmic microwave anisotropy multipoles. Because there is evidence for these phenomena, unexplained with ordinary CDM, an argument can be made that the dark matter is axions.

We study the applications of nonextensive Tsallis statistics to high energy and hadron physics. These applications include studies of $pp$ collisions, equation of state of QCD, as well as Bose–Einstein condensation. We also analyze the connections of Tsallis statistics with thermofractals, and address some of the conceptual aspects of the fractal approach, which are expressed in terms of the renormalization group equation and the self-energy corrections to the parton mass. We associate these well-known concepts with the origins of the fractal structure in the quantum field theory.

The ordered state and the elementary excitations are theoretically studied in an interacting dilute quasi-two-dimensional Bose gas of excitons in a type-II quantum well. This system is advantageous for studying the macroscopic quantum phenomena because those excitons have a long lifetime of the order of 10^-6 s, and their transport mechanism can be directly studied in experiments by observing electric current since the excitons consist of spatially separated electron-hole pairs. Using the obtained dispersion relations for excitations, we examine the Landau criterion for exciton superflow and the temperature dependence of the off-diagonal long-range order which characterizes the quasi-Bose-Einstein condensation in two-dimensional systems.

We show within the framework of Variational Path Integration that the density matrix and the ground state energy of the trapped Bose gas can be obtained in a simple way and it is in agreement with the result obtained by the variational Gross–Pitaevskii equation. The advantage of this method is the analytical result can be found for various forms of interaction between particles.

By studying the critical properties of a 2D Bose–Einstein condensation (BEC) in traps, we obtain the accurate analytic expressions of transition temperature, condensed fraction, and specific heat. The analytic results fit in fairly well with numerical results. We find that an isotropical potential favors most for condensation to occur. With the aid of Bloch summation, we study the distributions of coordinates and momenta of the system. Some clear physical pictures are presented.

We present a brief review of our recent results concerning non-mean-field effects of laser-induced dipole–dipole interactions on static and dynamical properties of atomic Bose–Einstein condensates.

Though commonly unrecognized, a superconducting BCS condensate consists of equal numbers of two-electron (2e) and two-hole (2h) Cooper pairs (CPs). A new complete (in the sense that 2h-CPs are not ignored) boson-fermion statistical ternary gas model, however, is able to depart from this perfect 2e-/2h-CP symmetry. It yields robustly higher T_c's without abandoning electron-phonon dynamics, and reduces to all the known statistical theories of superconductors, including the BCS-Bose "crossover" picture—but goes considerably beyond it.