arXiv subjects

A. A. Shanenko

Publications and source records attributed to A. A. Shanenko.

At least 55 records · Page 3Linked to original sources

arXiv2009

Giant Variations of Cooper-Pair Size in Nanoscale Superconductors

The Cooper-pair size (i.e., the BCS coherence length) in low-dimensional superconductors is dramatically modified by quantum-size effects. In particular, for nanowires made of conventional superconducting materials, we show that the coherence length exhibits size-dependent drops by two-three orders of magnitude and reaches values found in high-$T_c$ superconductors. This phenomenon is surprisingly similar to the well-known BCS-BEC crossover but with one important exception: it is driven by the transverse quantization of the electron spectrum rather than by the strength of the fermion-fermion interaction. Similar results can be expected for other systems with the same structure of the single-particle spectrum, e.g, for superfluid Fermi gases confined in a quantum-wire or quantum-well geometry.

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arXiv2009

Superconducting nanowires: quantum confinement and spatially dependent Hartree-Fock potential

It is well-known that in bulk, the solution of the Bogoliubov-de Gennes equations is the same whether or not the Hartree-Fock term is included. Here the Hartree-Fock potential is position independent and, so, gives the same contribution to both the single-electron energies and the Fermi level (the chemical potential). Thus, the single-electron energies measured from the Fermi level (they control the solution) stay the same. It is not the case for nanostructured superconductors, where quantum confinement breaks the translational symmetry and results in a position dependent Hartree-Fock potential. In this case its contribution to the single-electron energies depends on the relevant quantum numbers. We numerically solved the Bogoliubov-de Gennes equations with the Hartree-Fock term for a clean superconducting nanocylinder and found a shift of the curve representing the thickness-dependent oscillations of the critical superconducting temperature to larger diameters.

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arXiv2009

Size-dependent enhancement of superconductivity in nanowires

A shape-dependent superconducting resonance can be expected when an energy level associated with the transverse motion in a wire passes through the Fermi surface. We show that the recently observed width-dependent increase of $T_c$ in ${\rm Al}$ and ${\rm Sn}$ nanowires is a consequence of this shape resonance effect.

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arXiv2008

Magnetic-field induced quantum-size cascades in superconducting nanowires

In high-quality nanowires, quantum confinement of the transverse electron motion splits the band of single-electron states in a series of subbands. This changes in a qualitative way the scenario of the magnetic-field induced superconductor-to-normal transition. We numerically solve the Bogoliubov-de Gennes equations for a clean metallic cylindrical nanowire at zero temperature in a parallel magnetic field and find that for diameters D < 10-15 nm, this transition occurs as a cascade of subsequent jumps in the order parameter (this is opposed to the smooth second-order phase transition in the mesoscopic regime). Each jump is associated with the depairing of electrons in one of the single-electron subbands. As a set of subbands contribute to the order parameter, the depairing process occurs as a cascade of jumps. We find pronounced quantum-size oscillations of the critical magnetic field with giant resonant enhancements. In addition to these orbital effects, the paramagnetic breakdown of Cooper pairing also contributes but only for smaller diameters, i. e., D < 5 nm.

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arXiv2005

Shape resonances in the superconducting order parameter of ultrathin nanowires

We study the shape resonance effect associated with the confined transverse superconducting modes of a cylindrical nanowire in the clean limit. Results of numerical investigations of the Bogoliubov-de Gennes equations show significant deviations of the energy gap parameter from its bulk value with a profound effect on the transition temperature. The most striking is that the size of the resonances is found to be by about order of magnitude larger than in ultrathin metallic films with the same width.

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arXiv2004

Dilute Fermi gas: kinetic and interaction energies

A dilute homogeneous 3D Fermi gas in the ground state is considered for the case of a repulsive pairwise interaction. The low-density (dilution) expansions for the kinetic and interaction energies of the system in question are calculated up to the third order in the dilution parameter. Similar to the recent results for a Bose gas, the calculated quantities turn out to depend on a pairwise interaction through the two characteristic lengths: the former, $a$, is the well-known s-wave scattering length, and the latter, $b$, is related to $a$ by $b=a-m (\partial a/\partial m)$, where $m$ stands for the fermion mass. To take control of the results, calculations are fulfilled in two independent ways. The first involves the Hellmann-Feynman theorem, taken in conjunction with a helpful variational theorem for the scattering length. This way is used to derive the kinetic and interaction energies from the familiar low-density expansion of the total system energy first found by Huang and Yang. The second way operates with the in-medium pair wave functions. It allows one to derive the quantities of interest``from the scratch'', with no use of the total energy. An important result of the present investigation is that the pairwise interaction of fermions makes an essential contribution to their kinetic energy. Moreover, there is a complicated and interesting interplay of these quantities.

cond-mat.stat-mech↗

arXiv2002

Towards thermodynamical consistency of qusiparticle picture

The purpose of the present article is to call attention to some realistic quasiparticle-based description of the quark/gluon matter and its consistent implementation in thermodynamics. A simple and transparent representation of the thermodynamical consistency conditions is given. This representation allows one to review critically and systemize available phenomenological approaches to the deconfinement problem with respect to their thermodynamical consistency. A particular attention is paid to the development of a method for treating the string screening in the dense matter of unbound color charges. The proposed method yields an integrable effective pair potential which can be incorporated into the mean-field picture. The results of its application are in reasonable agreement with lattice data on the QCD thermodynamics.

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arXiv2001

The kinetic and interaction energies of a trapped Bose gas: Beyond the mean field

The kinetic and interaction energies of a three-dimensional dilute ground-state Bose gas confined in a trap are calculated beyond a mean-field treatment. They are found to depend on the pairwise interaction trough two characteristic lengths: the first, a, is the well-known scattering length and the second, b, is related to the latter by b=a-λd a/dλwith λbeing the coupling constant. Numerical estimations show that the pairwise interaction energy of a dilute gas of alkali atoms in a trap is negative (in spite of the positive scattering length); its absolute value is found by about the order of magnitude larger than that of the mean-field interaction energy that corresponds to the last term in the Gross-Pitaevskii functional.

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arXiv2001

Dilute Bose gas in two dimensions: Density expansions and the Gross-Pitaevskii equation

A dilute two-dimensional (2D) Bose gas at zero temperature is studied by the method developed earlier by the authors. Low density expansions are derived for the chemical potential, ground state energy, kinetic and interaction energies. The expansion parameter is found to be a dimensionless in-medium scattering amplitude u obeying the equation 1/u+\ln u=-\ln(na^2π)-2γ, where na^2 and γare the gas parameter and the Euler constant, respectively. It is shown that the ground state energy is mostly kinetic in the low density limit; this result does not depend on a specific form of the pairwise interaction potential, contrary to 3D case. A new form of 2D Gross-Pitaevskii equation is proposed within our scheme.

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arXiv2000

Dilute Bose gas: short-range particle correlations and ultraviolet divergence

The modified Bogoliubov model where the primordial interaction is replaced by the t matrix is reinvestigated. It is shown to provide a negative value of the kinetic energy for a strongly interacting dilute Bose gas, contrary to the original Bogoliubov model. To clear up the origin of this failure, the correct values of the kinetic and interaction energies of a dilute Bose gas are calculated. It is demonstrated that both the problem of the negative kinetic energy and the ultraviolet divergence, dating back to the well-known paper of Lee, Yang and Huang, is connected with an inadequate picture of the short-range boson correlations. These correlations are reconsidered within the thermodynamically consistent model proposed earlier by the present authors. Found results are in absolute agreement with the data of the Monte-Carlo calculations for the hard-sphere Bose gas.

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arXiv2000

Dynamical interpretation of chemical freeze-out in heavy ion collisions

It is demonstrated that there exists a direct correlation between chemical freeze-out point and the softest point of the equation of state where the pressure divided by the energy density, $p(ε)/ε$, has a minimum. A dynamical model is given as an example where the passage of the softest point coincides with the condition for chemical freeze-out, namely an average energy per hadron $\approx$ 1 GeV. The sensitivity of the result to the equation of state used is discussed.

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arXiv2000

Directed Flow of Baryons in Heavy-Ion Collisions

The collective motion of nucleons from high-energy heavy-ion collisions is analyzed within a relativistic two-fluid model for different equations of state (EoS). As function of beam energy the theoretical slope parameter F_y of the differential directed flow is in good agreement with experimental data, when calculated for the QCD-consistent EoS described by the statistical mixed-phase model. Within this model, which takes the deconfinement phase transition into account, the excitation function of the directed flow turns out to be a smooth function in the whole range from SIS till SPS energies. This function is close to that for pure hadronic EoS and exhibits no minimum predicted earlier for a two-phase bag-model EoS. Attention is also called to a possible formation of nucleon antiflow (F_y < 0) at energies of the order of 100 A GeV.

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arXiv2000

Short-range particle correlations in dilute Bose gas

The thermodynamics of a homogeneous dilute Bose gas with an arbitrary strong repulsion between particles is investigated on the basis of the exact relation connecting the pair correlation function with the in-medium pair wave functions and occupation numbers. It is shown that the effective-interaction scheme which is reduced to the Bogoliubov model with the effective pairwise potential, is not acceptable for investigating the short-range particle correlations in a dilute strongly interacting Bose gas. In contrast to this scheme, our model is thermodynamically consistent and free of the ultraviolet divergences due to accurate treatment of the short-range boson correlations. The equation for the in-medium scattering amplitude is derived that makes it possible to find the in-medium renormalization for the pair wave functions at short boson separations. Low-density expansions for the main thermodynamic quantities are reinvestigated on the basis of this equation. Besides, the expansions are found for the interaction and kinetic energies per particle. It is demonstrated that for the many-boson system of the hard spheres the interaction energy is equal to zero for any boson density. The exact relationship between the chemical potential and in-medium pair wave functions is also established.

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arXiv1999

Towards Strong-Coupling Generalization of the Bogoliubov Model

The well-known results concerning a dilute Bose gas with the short-range repulsive interaction should be reconsidered due to a thermodynamic inconsistency of the method being basic to much of the present understanding of this subject and nonrelevant behaviour of the pair distribution function at small boson separations. The aim of our paper is to propose a new way of treating the dilute Bose gas with an arbitrary strong interaction. Using the reduced density matrix of the second order and a variational procedure, this way allows us to escape the inconsistency mentioned and operate with singular potentials like the Lennard-Jones one. All the consideration concerns the zero temperature.

cond-mat.stat-mech↗

arXiv1999

Dynamical Interpretation of Chemical Freeze-Out Parameters

It is shown that the condition for chemical freeze-out, average energy per hadron approximately 1 GeV, selects the softest point of the equation of state, namely the point where the pressure divided by the energy density has a minimum. The sensitivity to the equation of state used is discussed. The previously proposed mixed phase model, which is consistent with lattice QCD data naturally leads to the chemical freeze-out condition.

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arXiv1999

On the 'Strong-Coupling' Generalization of the Bogoliubov Model

A generalized Bogoliubov model of the Bose gas in the ground state is proposed which properly takes into account both the long-range and short-range spatial boson correlations. It concerns equilibrium characteristics and operates with in-medium Schrodinger equations for the pair wave functions of bosons being the eigenfunctions of the second-order reduced density matrix. The approach developed provides reasonable results for a dilute Bose gas with arbitrary strong interaction between particles (the 'strong-coupling' case) and comes to the canonical Bogoliubov model in the weak-coupling regime.

cond-mat.stat-mech↗

arXiv1999

The Dilute Bose Gas Revised

The well-known results concerning a dilute Bose gas with the short-range repulsive interaction should be reconsidered due to a thermodynamic inconsistency of the method being basic to much of the present understanding of this subject. The aim of our paper is to propose a new way of treating the dilute Bose gas with an arbitrary strong interaction. Using the reduced density matrix of the second order and a variational procedure, this way allows us to escape the inconsistency mentioned and operate with singular potentials of the Lennard-Jones type. The derived expansion of the condensate depletion in powers of the boson density n=N/V reproduces the familiar result, while the expansion for the mean energy per particle is of the new form: E=2π\hbar^2 a n/m [1+128/(15 \sqrtπ)\sqrt{na^3}(1-5b/8a)+ ...], where a is the scattering length and b>0 stands for one more characteristic length depending on the shape of the interaction potential (in particular, for the hard spheres a=b). All the consideration concerns the zero temperature.

cond-mat.stat-mech↗

arXiv1999

Bound pair states beyond the condensate for Fermi systems below T_c: the pseudogap as a necessary condition

As is known, the 1/q^2 theorem of Bogoliubov asserts that the mean density of the fermion pair states with the total momentum q obeys the inequality n_q > C/q^2 (q \to 0) in the case of the Fermi system taken at nonzero temperature and in the superconducting state provided the interaction term of its Hamiltonian is locally gauge invariant. With the principle of correlation weakening it is proved in this paper that the reason for the mentioned singular behaviour of n_q is the presence of the bound states of particle pairs with nonzero total momenta. Thus, below the temperature of the superconducting phase transition there always exist the bound states of the fermion couples beyond the pair condensate. If the pseudogap observed in the normal phase of the high-T_c superconductors is stipulated by the presence of the electron bound pairs, then the derived result suggests, in a model-independent manner, that the pseudogap survives below T_c.

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