arXiv subjects

M. A. Solís

Publications and source records attributed to M. A. Solís.

30 records · Page 2Linked to original sources

arXiv2011

Boson gas in a periodic array of tubes

We report the thermodynamic properties of an ideal boson gas confined in an infinite periodic array of channels modeled by two, mutually perpendicular, Kronig-Penney delta-potentials. The particle's motion is hindered in the x-y directions, allowing tunneling of particles through the walls, while no confinement along the z direction is considered. It is shown that there exists a finite Bose- Einstein condensation (BEC) critical temperature Tc that decreases monotonically from the 3D ideal boson gas (IBG) value $T_{0}$ as the strength of confinement $P_{0}$ is increased while keeping the channel's cross section, $a_{x}a_{y}$ constant. In contrast, Tc is a non-monotonic function of the cross-section area for fixed $P_{0}$. In addition to the BEC cusp, the specific heat exhibits a set of maxima and minima. The minimum located at the highest temperature is a clear signal of the confinement effect which occurs when the boson wavelength is twice the cross-section side size. This confinement is amplified when the wall strength is increased until a dimensional crossover from 3D to 1D is produced. Some of these features in the specific heat obtained from this simple model can be related, qualitatively, to at least two different experimental situations: $^4$He adsorbed within the interstitial channels of a bundle of carbon nanotubes and superconductor-multistrand-wires Nb$_{3}$Sn.

cond-mat.quant-gas↗

arXiv2010

Dimensional crossover of a boson gas in multilayers

We obtain the thermodynamic properties for a non-interacting Bose gas constrained on multilayers modeled by a periodic Kronig-Penney delta potential in one direction and allowed to be free in the other two directions. We report Bose-Einstein condensation (BEC) critical temperatures, chemical potential, internal energy, specific heat, and entropy for different values of a dimensionless impenetrability $P\geqslant 0$ between layers. The BEC critical temperature $T_{c}$ coincides with the ideal gas BEC critical temperature $T_{0}$ when $P=0$ and rapidly goes to zero as $P$ increases to infinity for any finite interlayer separation. The specific heat $C_{V}$ \textit{vs} $T$ for finite $P$ and plane separation $a$ exhibits one minimum and one or two maxima in addition to the BEC, for temperatures larger than $T_{c}$ which highlights the effects due to particle confinement. Then we discuss a distinctive dimensional crossover of the system through the specific heat behavior driven by the magnitude of $P$. For $T T_{c}$, it is evidenced by a broad minimum in $C_{V}(T)$.

cond-mat.quant-gas↗

arXiv2007

Improved Quantum Hard-Sphere Ground-State Equations of State

The London ground-state energy formula as a function of number density for a system of identical boson hard spheres, corrected for the reduced mass of a pair of particles in a sphere-of-influence picture, and generalized to fermion hard-sphere systems with two and four intrinsic degrees of freedom, has a double-pole at the ultimate \textit{regular} (or periodic, e.g., face-centered-cubic) close-packing density usually associated with a crystalline branch. Improved fluid branches are contructed based upon exact, field-theoretic perturbation-theory low-density expansions for many-boson and many-fermion systems, appropriately extrapolated to intermediate densities, but whose ultimate density is irregular or \textit{random} closest close-packing as suggested in studies of a classical system of hard spheres. Results show substantially improved agreement with the best available Green-function Monte Carlo and diffusion Monte Carlo simulations for bosons, as well as with ladder, variational Fermi hypernetted chain, and so-called L-expansion data for two-component fermions.

cond-mat.stat-mech↗

arXiv2002

Anomalous behavior of ideal Fermi gas below two dimensions

Normal behavior of the thermodynamic properties of a Fermi gas in $d>2$ dimensions, integer or not, means monotonically increasing or decreasing of its specific heat, chemical potential or isothermal sound velocity, all as functions of temperature. However, for $0 2$ (known as the Bose-Einstein condensation), it is nevertheless an intriguing structural anomaly which we exhibit in detail.

cond-mat.stat-mech↗

arXiv2002

Harmonically Trapped Quantum Gases

We solve the problem of a Bose or Fermi gas in $d$-dimensions trapped by $% δ\leq d$ mutually perpendicular harmonic oscillator potentials. From the grand potential we derive their thermodynamic functions (internal energy, specific heat, etc.) as well as a generalized density of states. The Bose gas exhibits Bose-Einstein condensation at a nonzero critical temperature $T_{c}$ if and only if $d+δ>2$, and a jump in the specific heat at $T_{c}$ if and only if $d+δ>4$. Specific heats for both gas types precisely coincide as functions of temperature when $d+δ=2$. The trapped system behaves like an ideal free quantum gas in $d+δ$ dimensions. For $δ=0$ we recover all known thermodynamic properties of ideal quantum gases in $d$ dimensions, while in 3D for $δ=$ 1, 2 and 3 one simulates behavior reminiscent of quantum {\it wells, wires}and{\it dots}, respectively.

cond-mat.stat-mech↗

arXiv2001

Pre-formed Cooper pairs and Bose-Einstein condensation in cuprate superconductors

A two-dimensional (2D) assembly of noninteracting, temperature-dependent, pre-formed Cooper pairs in chemical/thermal equilibrium with unpaired fermions is examined in a binary boson-fermion statistical model as the Bose-Einstein condensation (BEC) singularity temperature $T_{c}$ is approached from above. Compared with BCS theory (which is {\it not} a BEC theory) substantially higher $T_{c}$'s are obtained without any adjustable parameters, that fall roughly within the range of empirical $T_{c}$'s for quasi-2D cuprate superconductors.

cond-mat.supr-con↗

arXiv2001

Bose-Einstein condensation of nonzero-center-of-mass-momentum Cooper pairs

Cooper pair (CP) binding with both zero and nonzero center-of-mass momenta (CMM) is studied with a set of renormalized equations assuming a short-ranged (attractive) pairwise interfermion interaction. Expanding the associated dispersion relation in 2D in powers of the CMM, in weak-to-moderate coupling a term {\it linear} in the CMM dominates the pair excitation energy, while the quadratic behavior usually assumed in Bose-Einstein (BE)-condensation studies prevails for any coupling {\it only} in the limit of zero Fermi velocity when the Fermi sea disappears, i.e., in vacuum. In 3D this same behavior is observed numerically. The linear term, moreover, exhibits CP breakup beyond a threshold CMM value which vanishes with coupling. This makes all the excited (nonzero-CMM) BE levels with preformed CPs collapse into a single ground level so that a BCS condensate (where only zero CMM CPs are usually allowed) appears in zero coupling to be a special case in either 2D or 3D of the BE condensate of linear-dispersion-relation CPs.

cond-mat.supr-con↗

arXiv2001

Cooper pair dispersion relation in two dimensions

The Cooper pair binding energy {\it vs.} center-of-mass-momentum dispersion relation for Bose-Einstein condensation studies of superconductivity is found in two dimensions for a renormalized attractive delta interaction. It crosses over smoothly from a linear to a quadratic form as coupling varies from weak to strong.

cond-mat.str-el↗

arXiv2000

Statistical Model of Superconductivity in a 2D Binary Boson-Fermion Mixture

A two-dimensional (2D) assembly of noninteracting, temperature-dependent, composite-boson Cooper pairs (CPs) in chemical and thermal equilibrium with unpaired fermions is examined in a binary boson-fermion statistical model as the superconducting singularity temperature is approached from above. The model is derived from {\it first principles} for the BCS model interfermion interaction from three extrema of the system Helmholtz free energy (subject to constant pairable-fermion number) with respect to: a) the pairable-fermion distribution function; b) the number of excited (bosonic) CPs, i.e., with nonzero total momenta--usually ignored in BCS theory--and with the appropriate (linear, as opposed to quadratic) dispersion relation that arises from the Fermi sea; and c) the number of CPs with zero total momenta. Compared with the BCS theory condensate, higher singularity temperatures for the Bose-Einstein condensate are obtained in the binary boson-fermion mixture model which are in rough agreement with empirical critical temperatures for quasi-2D superconductors

cond-mat.supr-con↗

arXiv2000

Cooper pair dispersion relation for weak to strong coupling

Cooper pairing in two dimensions is analyzed with a set of renormalized equations to determine its binding energy for any fermion number density and all coupling assuming a generic pairwise residual interfermion interaction. \ Also considered are Cooper pairs (CPs) with nonzero center-of-mass momentum (CMM)--usually neglected in BCS theory--and their binding energy is expanded analytically in powers of the CMM up to quadratic terms. A Fermi-sea-dependent {\it linear} term in the CMM dominates the pair excitation energy in weak coupling (also called the BCS regime) while the more familiar quadratic term prevails in strong coupling (the Bose regime). The crossover, though strictly unrelated to BCS theory {\it per se,} is studied numerically as it is expected to play a central role in a model of superconductivity as a Bose-Einstein condensation of CPs where the transition temperature vanishes for all dimensionality $d\leq 2$ for quadratic dispersion, but is {\it nonzero} for all $d\geq 1$ for linear dispersion.

cond-mat.supr-con↗

arXiv2000

Low-dimensional BEC

The Bose-Einstein condensation (BEC) temperature $T_{c}$ of Cooper pairs (CPs) created from a very general interfermion interaction is determined for a {\it linear}, as well as the usual quadratic, energy {\it vs}% center-of-mass momentum dispersion relation. This $T_{c}$ is then compared to that of Wen & Kan (1988) in $d=2+ε$ dimensions, for small $ε$, in a geometry of an infinite stack of parallel (e.g., copper-oxygen) planes as in a cuprate, and with a new result for linear-dispersion CPs. This allows addressing, as a rough first approximation, superconductivity for any $d>1$.

cond-mat.supr-con↗

arXiv2000

Superconductivity as a Bose-Einstein condensation?

Bose-Einstein condensation (BEC) in two dimensions (2D) (e.g., to describe the quasi-2D cuprates) is suggested as the possible mechanism widely believed to underlie superconductivity in general. A crucial role is played by nonzero center-of-mass momentum Cooper pairs (CPs) usually neglected in BCS theory. Also vital is the unique {\it linear} dispersion relation appropriate to weakly-coupled "bosonic" CPs moving in the Fermi sea--rather than in vacuum where the dispersion would be quadratic but only for very strong coupling, and for which BEC is known to be impossible in 2D.

cond-mat.supr-con↗