1,219 research outputs found
Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
The formal algebraic structures that govern higher-spin theories within the
unfolded approach turn out to be related to an extension of the Kontsevich
Formality, namely, the Shoikhet-Tsygan Formality. Effectively, this allows one
to construct the Hochschild cocycles of higher-spin algebras that make the
interaction vertices. As an application of these results we construct a family
of Vasiliev-like equations that generate the Hochschild cocycles with
symmetry from the corresponding cycles. A particular case of may be
relevant for the on-shell action of the theory. We also give the exact
equations that describe propagation of higher-spin fields on a background of
their own. The consistency of formal higher-spin theories turns out to have a
purely geometric interpretation: there exists a certain symplectic invariant
associated to cutting a polytope into simplices, namely, the Alexander-Spanier
cocycle.Comment: typos fixed, many comments added, 36 pages + 20 pages of Appendices,
3 figure
Energy relaxation rate and its mesoscopic fluctuations in quantum dots
We analyze the applicability of the Fermi-golden-rule description of
quasiparticle relaxation in a closed diffusive quantum dot with
electron-electron interaction. Assuming that single-particle levels are already
resolved but the initial stage of quasiparticle disintegration can still be
described by a simple exponential decay, we calculate the average inelastic
energy relaxation rate of single-particle excitations and its mesoscopic
fluctuations. The smallness of mesoscopic fluctuations can then be used as a
criterion for the validity of the Fermi-golden-rule description. Technically,
we implement the real-space Keldysh diagram technique, handling correlations in
the quasi-discrete spectrum non-perturbatively by means of the non-linear
supersymmetric sigma model. The unitary symmetry class is considered for
simplicity. Our approach is complementary to the lattice-model analysis of Fock
space: thought we are not able to describe many-body localization, we derive
the exact lowest-order expression for mesoscopic fluctuations of the relaxation
rate, making no assumptions on the matrix elements of the interaction. It is
shown that for the quasiparticle with the energy on top of the
thermal state with the temperature , fluctuations of its energy width become
large and the Fermi-golden-rule description breaks down at
, where is the mean level
spacing in the quantum dot, and is its dimensionless conductance.Comment: 33 pages, 9 figure
Onset of superconductivity in a voltage-biased NSN microbridge
We study the stability of the normal state in a mesoscopic NSN junction
biased by a constant voltage V with respect to the formation of the
superconducting order. Using the linearized time-dependent Ginzburg-Landau
equation, we obtain the temperature dependence of the instability line,
V_{inst}(T), where nucleation of superconductivity takes place. For
sufficiently low biases, a stationary symmetric superconducting state emerges
below the instability line. For higher biases, the normal phase is destroyed by
the formation of a non-stationary bimodal state with two superconducting nuclei
localized near the opposite terminals. The low-temperature and large-voltage
behavior of the instability line is highly sensitive to the details of the
inelastic relaxation mechanism in the wire. Therefore, experimental studies of
V_{inst}(T) in NSN junctions may be used as an effective tool to access
parameters of the inelastic relaxation in the normal state.Comment: 5 pages, 2 figure
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