191 research outputs found
BCS ansatz, Bogoliubov approach to superconductivity and Richardson-Gaudin exact wave function
The Bogoliubov approach to superconductivity provides a strong mathematical
support to the wave function ansatz proposed by Bardeen, Cooper and Schrieffer
(BCS). Indeed, this ansatz --- with all pairs condensed into the same state ---
corresponds to the ground state of the Bogoliubov Hamiltonian. Yet, this
Hamiltonian only is part of the BCS Hamiltonian. As a result, the BCS ansatz
definitely differs from the BCS Hamiltonian ground state. This can be directly
shown either through a perturbative approach starting from the Bogoliubov
Hamiltonian, or better by analytically solving the BCS Schr\"{o}dinger equation
along Richardson-Gaudin exact procedure. Still, the BCS ansatz leads not only
to the correct extensive part of the ground state energy for an arbitrary
number of pairs in the energy layer where the potential acts --- as recently
obtained by solving Richardson-Gaudin equations analytically --- but also to a
few other physical quantities such as the electron distribution, as here shown.
The present work also considers arbitrary filling of the potential layer and
evidences the existence of a super dilute and a super dense regime of pairs,
with a gap \emph{different} from the usual gap. These regimes constitute the
lower and upper limits of density-induced BEC-BCS cross-over in Cooper pair
systems.Comment: 15 pages, no figure
Auxiliary field approach to dilute Bose gases with tunable interactions
We rewrite the Lagrangian for a dilute Bose gas in terms of auxiliary fields
related to the normal and anomalous condensate densities. We derive the loop
expansion of the effective action in the composite-field propagators. The
lowest-order auxiliary field (LOAF) theory is a conserving mean-field
approximation consistent with the Goldstone theorem without some of the
difficulties plaguing approximations such as the Hartree and Popov
approximations. LOAF predicts a second-order phase transition. We give a set of
Feynman rules for improving results to any order in the loop expansion in terms
of composite-field propagators. We compare results of the LOAF approximation
with those derived using the Popov approximation. LOAF allows us to explore the
critical regime for all values of the coupling constant and we determine
various parameters in the unitarity limit.Comment: 16 pages, 7 figure
On the relation between virial coefficients and the close-packing of hard disks and hard spheres
The question of whether the known virial coefficients are enough to determine
the packing fraction at which the fluid equation of state of a
hard-sphere fluid diverges is addressed. It is found that the information
derived from the direct Pad\'e approximants to the compressibility factor
constructed with the virial coefficients is inconclusive. An alternative
approach is proposed which makes use of the same virial coefficients and of the
equation of state in a form where the packing fraction is explicitly given as a
function of the pressure. The results of this approach both for hard-disk and
hard-sphere fluids, which can straightforwardly accommodate higher virial
coefficients when available, lends support to the conjecture that
is equal to the maximum packing fraction corresponding to an ordered
crystalline structure.Comment: 10 pages, 6 figures; v2: discussion about hard-square and
hard-hexagon systems on a lattice added; five new reference
Bernoulli potential in type-I and weak type-II supercoductors: II. Surface dipole
The Budd-Vannimenus theorem is modified to apply to superconductors in the
Meissner state. The obtained identity links the surface value of the
electrostatic potential to the density of free energy at the surface which
allows one to evaluate the electrostatic potential observed via the capacitive
pickup without the explicit solution of the charge profile.Comment: 7 pages, 1 figur
Exactly-Solvable Models Derived from a Generalized Gaudin Algebra
We introduce a generalized Gaudin Lie algebra and a complete set of mutually
commuting quantum invariants allowing the derivation of several families of
exactly solvable Hamiltonians. Different Hamiltonians correspond to different
representations of the generators of the algebra. The derived exactly-solvable
generalized Gaudin models include the Bardeen-Cooper-Schrieffer,
Suhl-Matthias-Walker, the Lipkin-Meshkov-Glick, generalized Dicke, the Nuclear
Interacting Boson Model, a new exactly-solvable Kondo-like impurity model, and
many more that have not been exploited in the physics literature yet
Multi-threshold second-order phase transition
We present a theory of the multi-threshold second-order phase transition, and
experimentally demonstrate the multi-threshold second-order phase transition
phenomenon. With carefully selected parameters, in an external cavity diode
laser system, we observe second-order phase transition with multiple (three or
four) thresholds in the measured power-current-temperature three dimensional
phase diagram. Such controlled death and revival of second-order phase
transition sheds new insight into the nature of ubiquitous second-order phase
transition. Our theory and experiment show that the single threshold
second-order phase transition is only a special case of the more general
multi-threshold second-order phase transition, which is an even richer
phenomenon.Comment: 5 pages, 3 figure
Scanning tunneling spectroscopy of high-temperature superconductors
Tunneling spectroscopy played a central role in the experimental verification
of the microscopic theory of superconductivity in the classical
superconductors. Initial attempts to apply the same approach to
high-temperature superconductors were hampered by various problems related to
the complexity of these materials. The use of scanning tunneling
microscopy/spectroscopy (STM/STS) on these compounds allowed to overcome the
main difficulties. This success motivated a rapidly growing scientific
community to apply this technique to high-temperature superconductors. This
paper reviews the experimental highlights obtained over the last decade. We
first recall the crucial efforts to gain control over the technique and to
obtain reproducible results. We then discuss how the STM/STS technique has
contributed to the study of some of the most unusual and remarkable properties
of high-temperature superconductors: the unusual large gap values and the
absence of scaling with the critical temperature; the pseudogap and its
relation to superconductivity; the unprecedented small size of the vortex cores
and its influence on vortex matter; the unexpected electronic properties of the
vortex cores; the combination of atomic resolution and spectroscopy leading to
the observation of periodic local density of states modulations in the
superconducting and pseudogap states, and in the vortex cores.Comment: To appear in RMP; 65 pages, 62 figure
Quarkonia and QGP studies
We summarize results of recent studies of heavy quarkonia correlators and
spectral functions at finite temperatures from lattice QCD and systematic
T-matrix studies using QCD motivated finite-temperature potentials. We argue
that heavy quarkonia dissociation shall occur in the temperature range by the interplay of both screening and absorption in the
strongly correlated plasma medium. We discuss these effects on the quantum
mechanical evolution of quarkonia states within a time-dependent harmonic
oscillator model with complex oscillator strength and compare the results with
data for from RHIC and SPS experiments. We
speculate whether the suppression pattern of the rather precise NA60 data from
In-In collisions may be related to the recently discovered X(3872) state.
Theoretical support for this hypothesis comes from the cluster expansion of the
plasma Hamiltonian for heavy quarkonia in a strongly correlated medium.Comment: 6 pages, 5 figures, contribution to the proceedings of QUARKONIUM
2010: Three Days Of Quarkonium Production in pp and pA Collisions, 29-31 July
2010, Palaiseau, Franc
Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality
We consider aspects of Chern-Simons theory on L(p,q) lens spaces and its
relation with matrix models and topological string theory on Calabi-Yau
threefolds, searching for possible new large N dualities via geometric
transition for non-SU(2) cyclic quotients of the conifold. To this aim we find,
on one hand, some novel matrix integral representations of the SU(N) CS
partition function in a generic flat background for the whole L(p,q) family and
provide a solution for its large N dynamics; on the other, we perform in full
detail the construction of a family of would-be dual closed string backgrounds
via conifold geometric transition from T^*L(p,q). We can then explicitly prove
that Gopakumar-Vafa duality in a fixed vacuum fails in the case q>1, and
briefly discuss how it could be restored in a non-perturbative setting.Comment: 17 pages, 6 figures; references adde
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