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The effective mass of Abrikosov vortices in superconductors remains a challenging problem with limited experimental verification. In this paper, we present a method based on observation of the vortex mass in magnetic circular dichroism at terahertz frequencies. We demonstrate the emergence of dichroism with decreasing temperature in two YBa$_2$Cu$_3$O$_{7-\delta}$ thin films of different doping. The experimental results can be explained within a theoretical model that takes into account the vortex mass and provides an expression for the optical complex conductivity. We discuss the model parameters and show how they are obtained from the supporting experiments., Comment: 5 pages, 3 figures

Mass of Abrikosov vortices defied experimental observation for more than four decades. We demonstrate a method of its detection in high-temperature superconductors. Similarly to electrons, fluxons circulate in the direction given by the magnetic field, causing circular dichroism. We report the magneto-transmittance of a nearly optimally doped thin YBaCuO film, measured using circularly polarized submillimeter waves. The circular dichroism emerges in the superconducting state and increases with dropping temperature. Our results confirm the dominant role of quasiparticle states in the vortex core and yield the diagonal fluxon mass of 2.2 x 10^8 electron masses per centimeter at 45 K and zero-frequency limit and even larger off-diagonal mass of 4.9 x 10^8 electron masses per centimeter., Comment: 5 pages 3 figures + Supplemental material 3 pages

We study how attractive boron correlations in boron-doped diamond affect the superconducting critical temperature. The critical temperature is obtained from the McMillan formula for strong coupling superconductors with the density of states evaluated in the dynamical cluster approximation. Numerical results for the cluster of $2\times 2\times 2$ atoms show that attractive correlations lower the density of states at the Fermi level. We argue that this might explain experimentally observed differences in critical temperatures of 100 and 111 oriented films.

According to the BCS theory the superconducting condensate develops in a single quantum mode and no Cooper pairs out of the condensate are assumed. Here we discuss a mechanism by which the successful mode inhibits condensation in neighboring modes and suppresses a creation of noncondensed Cooper pairs. It is shown that condensed and noncondensed Cooper pairs are separated by an energy gap which is smaller than the superconducting gap but large enough to prevent nucleation in all other modes and to eliminate effects of noncondensed Cooper pairs on properties of superconductors. Our result thus justifies basic assumptions of the BCS theory and confirms that the BCS condensate is stable with respect to two-particle excitations.

We discuss an effect of the electrostatic field on superconductivity near the surface. First, we use the microscopic theory of de Gennes to show that the electric field changes the boundary condition for the Ginzburg-Landau function. Second, the effect of the electric field is evaluated in the vicinity of $H_{\rm c3}$, where the boundary condition plays a crucial role. We predict that the field effect on the surface superconductivity leads to a discontinuity of the magnetocapacitance. We estimate that the predicted discontinuity is accessible for nowadays experimental tools and materials. It is shown that the magnitude of this discontinuity can be used to predict the dependence of the critical temperature on the charge carrier density which can be tailored by doping., Comment: Book chapter world scientific; Hardcover, ISBN: 978-3-642-15136-1

We remove a self-interaction from the Galitskii-Feynman T-matrix approximation. This correction has no effect in the normal state but makes the theory applicable to the superconducting state. It is shown that identical theory is obtained by removing nonphysical repeated collisions in the spirit of the Fadeev-Watson-Lovelace multiple scattering expansion. Our correction does not violate the two-particle symmetry of the T-matrix, therefore the present theory is conserving in the Baym-Kadanoff sense. The theory is developed for retarded interactions leading to the Eliashberg theory in the approximation of a single pairing channel., Comment: 4 pages, 2 figures

Electrostatic charging changes the critical temperature of superconducting thin layers. To understand the basic mechanism, it is possible to use the Ginzburg-Landau theory with the boundary condition derived by de Gennes from the BCS theory. Here we show that a similar boundary condition can be obtained from the principle of minimum free energy. We compare the two boundary conditions and use the Budd-Vannimenus theorem as a test of approximations., Comment: 6 pages, 4 figures

Interaction of the superconducting condensate with deformations of the crystal lattice is formulated assuming the electrostatic potential of Bernoulli type and the effect of strain on material parameters. In the isotropic approximation it is shown that within the Ginzburg-Landau theory both contributions can be recast into the local but non-linear interaction term of the free energy., Comment: 6 pages

In superconductors penetrated by Abrikosov vortices the magnetic pressure and the inhomogeneous condensate density induce a deformation of the ionic lattice. We calculate how this deformation corrugates the surface of a semi-infinite sample. The effect of the surface dipole is included.

The interaction of the ionic lattice with the superconducting condensate is treated in terms of the electrostatic force in superconductors. It is shown that this force is similar but not identical to the force suggested by the volume difference of the normal and superconducting states. The BCS theory shows larger deviations than the two-fluid model., Comment: 6 pages no figures

The correlated density appears in many physical systems ranging from dense interacting gases up to Fermi liquids which develop a coherent state at low temperatures, the superconductivity. One consequence of the correlated density is the Bernoulli potential in superconductors which compensates forces from dielectric currents. This Bernoulli potential allows to access material parameters. Though within the surface potential these contributions are largely canceled, the bulk measurements with NMR can access this potential. Recent experiments are explained and new ones suggested. The underlying quantum statistical theory in nonequilibrium is the nonlocal kinetic theory developed earlier., Comment: 14 pages, CMT30 proceedings

Deformation of the superconductor crystal lattice caused by Abrikosov vortices is formulated as a response of the elastic crystal lattice to electrostatic forces. It is shown that the lattice compression is linearly proportional to the electrostatic potential known as the Bernoulli potential. Eventual consequences of the crystal lattice deformation on the effective vortex mass are discussed., Comment: 4 pages 5 figures

The electrostatic potential above the Abrikosov vortex lattice, discussed earlier by Blatter {\em et al.} {[}PRL {\bf 77}, 566 (1996){]}, is evaluated within the Ginzburg-Landau theory. Unlike previous studies we include the surface dipole. Close to the critical temperature, the surface dipole reduces the electrostatic potential to values below a sensitivity of recent sensors. At low temperatures the surface dipole is less effective and the electrostatic potential remains observable as predicted earlier., Comment: 8 pages 5 figures

The thermopower of superconductors measured via the magnetic flux in bimetallic loop is evaluated. It is shown that by a standard matching of the electrostatic potential, known as the Bernoulli potential, one explains the experimentally observed amplitude and the divergence in the vicinity of the critical temperature., Comment: 4 pages, 2 figures

For type II superconductors, Josephson has shown that vortices moving with velocity v_L create an effective electric field E'=-v_L x B. By definition the effective electric field is gradient of the electrochemical potential, what is the quantity corresponding to voltage observed with the use of Ohmic contacts. It relates to the true electric field E via the local chemical potential mu as E'=E - grad(mu)/e. We argue that at low temperatures the true electric field in the bulk can be approximated by a modified Josephson relation E=(v_s-v_L) x B, where v_S is the condensate velocity., Comment: 3 pages

The Budd-Vannimenus theorem is modified to the surface of superconductors in the Meissner state. This identity links the surface value of the electrostatic potential to the free energy in the bulk which allows one to evaluate the observed potential without the explicit solution of the charge profile at the surface., Comment: 4 pages 1 figure

The NMR and NQR spectra of $^{63}$Cu in the CuO$_2$ plane of YBa$_2$Cu$_3$O$_7$ in the superconducting state are discussed in terms of the phenomenological theory of Ginzburg-Landau type extended to lower temperatures. We show that the observed spectra, Kumagai {\em et al.}, PRB {\bf 63}, 144502 (2001), can be explained by a standard theory of the Bernoulli potential with the charge transfer between CuO$_2$ planes and CuO chains assumed., Comment: 11 pages 7 figures

The electrostatic potential in the flat superconducting slab is evaluated in the framework of the Ginzburg-Landau theory extended by Bardeen to low temperatures. For magnetic fields below B_c1, we discuss the formation of a surface charge induced by the Bernoulli potential of the suppercurrents., Comment: 6 pages, 5 figures

The electrostatic potential in a superconductor is studied. To this end Bardeen's extension of the Ginzburg-Landau theory to low temperatures is used to derive three Ginzburg-Landau equations - the Maxwell equation for the vector potential, the Schroedinger equation for the wave function and the Poisson equation for the electrostatic potential. The electrostatic and the thermodynamic potential compensate each other to a great extent resulting into an effective potential acting on the superconducting condensate. For the Abrikosov vortex lattice in Niobium, numerical solutions are presented and the different contributions to the electrostatic potential and the related charge distribution are discussed., Comment: 19 pages, 11 figures

The electrostatic Bernoulli potential measured at the surface of a superconductor via Kelvin capacitive coupling is shown to be independent of the pairing mechanism. This contrasts with the Bernoulli potential in the bulk where contributions due to pairing dominate close to $T_c$., Comment: 2 pages

It is generally accepted that vortex core is charged, what illustrates that even in stationary superconductors electric field may be present. Vortex structure and other properties of superconductors are usually calculated in the framework of the Ginzburg-Landau theory, which does not cover electric field. We show that the generalization of the GL theory due to Bardeen allows one to derive a third GL equation for the electrostatic potential. Since the Bardeen theory applies to all temperatures, the presented theory enables one to calculate charge profiles of the vortex under quite general conditions. The theory is consistent with the BCS-Gorkov results., Comment: 3 pages, New3SC-3 conference

The non-local scattering-in and -out integrals of the Enskog equation have reversed displacements of colliding particles reflecting that the -in and -out processes are conjugated by the space and time inversions. Generalisations of the Enskog equation to Fermi liquid systems are hindered by a request of the particle-hole symmetry which contradicts the reversed displacements. We resolve this problem with the help of the optical theorem. It is found that space-time and particle-hole symmetry can only be fulfilled simultaneously for the Bruckner-type of internal Pauli-blocking while the Feynman-Galitskii form allows only for particle-hole symmetry but not for space-time symmetry due to a stimulated emission of Bosons.

The charge density distribution with respect to the velocity of matter produced in peripheral heavy ion reactions around Fermi energy is investigated. The experimental finding of enhancement of mid-rapidity matter shows the necessity to include correlations beyond BUU which was performed in the framework of nonlocal kinetic theory. Different theoretical improvements are discussed. While the in-medium cross section changes the number of collisions, it leaves the transferred energy almost unchanged. In contrast the nonlocal scenario changes the energy transferred during collisions and leads to an enhancement of mid-rapidity matter. The renormalisation of quasiparticle energies can be included in nonlocal scenarios and leads to a further enhancement of mid-rapidity matter distribution. This renormalisation is accompanied by a dynamical softening of the equation of state seen in longer oscillation periods of the excited compressional collective mode. We propose to include quasiparticle renormalisation by using the Pauli-rejected collisions which circumvent the problem of backflows in Landau theory. Using the maximum relative velocity of projectile and target like fragments we associate experimental events with impact parameters of the simulations. For peripheral collisions we find a reasonable agreement between experiment and theory. For more central collisions, the velocity damping is higher in one-body simulations than observed experimentally, because of missing cluster formations in the kinetic theory used., Comment: citations completed, formulae corrected

The time dependent Schroedinger equation is solved analytically for a simplified model of moving infinite walls. A new knock-out mode is described which might occur during heavy ion collisions. The outer shell-nucleons are ionised due to the increase of level energy when two nuclei are approaching fast enough. This is analogous to the Mott effect but in contrast occurs only if the reaction time is short enough that no common ionisation threshold in the compound system is established. To demonstrate this pure nonequilibrium effect a simulation of realistic heavy ion collision by a nonlocal Boltzmann equation is performed., Comment: final corrections

The finite duration of the collisions in Fermionic systems as expressed by the retardation time in non-Markovian Levinson-type kinetic equations is discussed in the quasiclassical limit. We separate individual contributions included in the memory effect resulting in (i) off-shell tails of the Wigner distribution, (ii) renormalization of scattering rates and (iii) of the single-particle energy, (iv) collision delay and (v) related non-local corrections to the scattering integral. In this way we transform the Levinson equation into the Landau-Silin equation extended by the non-local corrections known from the theory of dense gases. The derived nonlocal kinetic equation unifies the Landau theory of quasiparticle transport with the classical kinetic theory of dense gases. The space-time symmetry is discussed versus particle-hole symmetry and a solution is proposed which transforms these two exclusive pictures into each other., Comment: slightly revised, 19 pages

The short time behavior of a disturbed system is influenced by off-shell motion and best characterized by the reduced density matrix possessing high energetic tails. We present analytically the formation of correlations due to collisions in an interacting Fermionic system with and without initial correlation. After this short time regime the time evolution is controlled by small gradients. This leads to a nonlocal Boltzmann equation for the quasiparticle distribution and a functional relating the latter one to the reduced density matrix. The nonlocalities are presented as time and space shifts arising from gradient expansion and are leading to virial corrections in the thermodynamical limit., Comment: Proceedings KB99 Workshop, September 20-24 1999, Rostock, Germany

Binary collisions in Fermi systems obey two fundamental symmetries corresponding to the space and time inversion and to the interchange of particles and holes. We show that beyond the local and instant approximation of scattering-in and -out integrals of a kinetic equation, only one of symmetries can be explicit while the other has to be covered by a constraint. This constraint, derived from the optical theorem, allows one to convert at need an explicit particle-hole symmetric form to the space-time symmetric form and vice versa. We implement this constraint to heavy ion reactions, where simulation algorithms require the space-time symmetry while former theories offer kinetic equations with the explicit particle-hole symmetry., Comment: Phys. Rev. Lett

The kinetic theory recently implemented in heavy ion reactions combines a non-local and non-instant picture of binary collisions with quasiparticle features. We show that the non-instant description is compatible with the spectral concept of quasiparticles while the commonly used variational concept is consistent only with instant collisions. The rearrangement energy, by which the variational concept surpasses the spectral one, is shown to be covered by a medium effect on non-instant collisions., Comment: PRE 59,1 rap. comm

For a set of realistic nucleon-nucleon potentials we evaluate microscopic parameters of binary collisions: a time duration of the scattering state, a mean distance and a rotation of nucleons during a collision. These parameters enter the kinetic equation as non-instantaneous and non-local corrections of the scattering integral, i.e., they can be experimentally tested. Being proportional to off-shell derivatives of the scattering T-matrix, non-instantaneous and non-local corrections make it possible to compare the off-shell behavior of different potentials in a vicinity of the energy shell. The Bonn one-Boson-exchange (A-C) and Paris potentials are found to yield very close results, while the separable Paris potential differs., Comment: Phys. Rev. C sub

A kinetic equation which combines the quasiparticle drift of Landau's equation with a dissipation governed by a nonlocal and noninstantaneous scattering integral in the spirit of Enskog corrections is discussed. Numerical values of the off-shell contribution to the Wigner distribution, of the collision duration and of the collision nonlocality are presented for different realistic potentials. On preliminary results we show that simulations of quantum molecular dynamics extended by the nonlocal treatment of collisions leads to a broader proton distribution bringing the theoretical spectra closer towards the experimental values than the local approach., Comment: Proceedings of the Erice School, published as Vol. 42 of "Progress in Particle and Nuclear Physics" by ELSEVIER

Within QMD simulations we demonstrate the effect of virial corrections on heavy ion reactions. Unlike in standard codes, the binary collisions are treated as non-local so that the contribution of the collision flux to the reaction dynamics is covered. A comparison with standard QMD simulations shows that the virial corrections lead to a broader proton distribution bringing theoretical spectra closer towards experimental values. Complementary BUU simulations reveal that the non-locality enhances the collision rate in the early stage of the reaction. It suggests that the broader distribution appears due to an enhanced pre-equilibrium emission of particles.

The damping of hot giant dipole resonances is investigated. The contribution of surface scattering is compared with the contribution from interparticle collisions. A unified response function is presented which includes surface damping as well as collisional damping. The surface damping enters the response via the Lyapunov exponent and the collisional damping via the relaxation time. The former is calculated for different shape deformations of quadrupole and octupole type. The surface as well as the collisional contribution each reproduce almost the experimental value, therefore we propose a proper weighting between both contributions related to their relative occurrence due to collision frequencies between particles and of particles with the surface. We find that for low and high temperatures the collisional contribution dominates whereas the surface damping is dominant around the temperatures $\sqrt{3}/2\pi$ of the centroid energy., Comment: PRC sub

A kinetic equation which combines the quasiparticle drift of Landau's equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Snider's equation for gases is derived. Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second order quantum virial corrections. The medium effects on binary collisions are shown to mediate the latent heat, i.e., an energy conversion between correlation and thermal energy. An implementation to heavy ion collisions is discussed.

For a system of non-interacting electrons scattered by neutral impurities, we derive a modified Boltzmann equation that includes quasiparticle and virial corrections. We start from quasiclassical transport equation for non-equilibrium Green's functions and apply limit of small scattering rates. Resulting transport equation for quasiparticles has gradient corrections to scattering integrals. These gradient corrections are rearranged into a form characteristic for virial corrections.

For a system of non-interacting electrons scattered by resonant levels of neutral impurities, we show that virial and quasiparticle corrections have nearly equal magnitudes. We propose a modification of the Boltzmann equation that includes quasiparticle and virial corrections and discuss their interplay on a dielectric function.

The formation of binary correlations in plasma is studied from the quantum kinetic equation. It is shown that this formation is much faster than dissipation due to collisions, in hot (dense) plasma the correlations form on the timescale of inverse plasma frequency (Fermi energy). This hierarchy of characteristic times is used to derive analytical formulae for time dependency of the potential energy of binary interactions which measures the extent of correlations. We discuss the dynamical formation of screening and compare with the statical screened result.Comparisons are made with molecular dynamic simulations. In the low temperature limit we find an analytical expression for the formation of correlation which is general for any binary interaction. It can be applied in nuclear situations as well as dense metals., Comment: Phys. Lett. A sub