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In this work, a new functional is introduced to treat pairing correlations in finite many-body systems. Guided by the projected BCS framework, the energy is written as a functional of occupation numbers. It is shown to generalize the BCS approach and to provide an alternative to Variation After Projection framework. Illustrations of the new approach are given for the pairing Hamiltonian for various particle numbers and coupling strengths. In all case, a very good agreement with the exact solution is found.

Buttiker–Thomas–Pretre (BTP) [Z. Phys.B94, 133 (1994)] proposed that the concepts behind the Larmor precession time tell us that it is possible to define exactly the local density of states (LDOS) in terms of the scattering matrix. However, we take into account evanescent modes and show that for an impurity in a quantum wire, this is in principle not exactly true. We also prove that the Wigner delay time gives correct superluminal times at the Fano resonances, in spite of the fact that the stationary phase approximation is not valid there.

We propose a kinetic theory of transport in metals embedded with ferromagnetic nanoclusters, predicting a quadratic low-field magnetoresistance in an ensemble of clusters in thermodynamic equilibrium. We show that this effect is strongest when all the clusters have the same intrinsic easy-axis anisotropy.

The intrinsic spin Hall effect has been attracting increasing theoretical and experimental interest since its discovery about two years ago. In this article, we review the main achievements in the theoretical aspect of both dissipative and nondissipative spin Hall effects in mesoscopic systems. The Landauer–Büttiker formula and Green's function approach based numerical method for the spin Hall effect is also introduced.

Shape phase transitions in nuclei, an example of quantum phase transitions in mesoscopic systems, are briefly reviewed. Spectral signatures of critical points in finite quantal systems are discussed and experimental examples are shown.

We introduce a characteristic function method to describe charge-counting statistics (CCS) in phase coherent systems that directly connects the three most successful approaches to quantum transport: random-matrix theory (RMT), the nonlinear σ-model and the trajectory-based semiclassical method. The central idea is the construction of a generating function based on a multivariate hypergeometric function, which can be naturally represented in terms of quantities that are well-defined in each approach. We illustrate the power of our scheme by obtaining exact analytical results for the first four cumulants of CCS in a chaotic quantum dot coupled ideally to electron reservoirs via perfectly conducting leads with arbitrary number of open scattering channels.

In this paper, we study the dynamics of a quantum two-mesh LC circuit with discrete charge subject to rapidly oscillating voltage sources. A time-independent effective Hamiltonian for this system is derived in a high-frequency series expansion upto ${\omega }^{-2}$ whose dominant behavior indicates the possibility of observing two physical phenomena: first, the controlled manipulation and suppression of the mesh currents by setting specific values of the voltage source amplitudes and, second, the onset of a DC regime (in the single–mesh case) which could be inferred by interpreting the quasi-degenerate quantum states.

In the present work, we consider a quantum LC circuit under a constant magnetic field. In particular, we derive a new discretized form of the Schrödinger equation, which is equivalent to introducing a potential in the pseudo-flux representation. We discuss the physical assumptions leading to our results, and using a direct numerical approach we calculate the energy spectrum of the LC quantum circuit as a function of a constant external magnetic flux. The results are compared with the spectrum obtained using the Li–Chen potential [Y. Q. Li and B. Chen, Phys. Rev. B 53 (1996) 4027]. Our results indicate that the energy spectra from both models are numerically different, hence they may be clearly distinguished under appropriate experimental conditions.

This paper reviews the method of bosonization for one-dimensional interacting fermions. Example of its application to mesoscopic systems is presented with an explicit calculation of the spin and charge currents in an interacting quantum wire subject to a uniform magnetic field and alternating voltage source. Special emphasis is given to the details of the calculation using bosonization and Keldysh techniques.

Mesoscopic capacitor theory, which includes intrinsic inductive effects from quantum tunneling, is applied to conducting spherical shells. The zero-point pressure and the number of virtual charged pairs are determined assuming a Poisson distribution. They are completely defined by a dimensionless mesoscopic parameter (χ_c) measuring the average number of virtual pairs per solid angle and carrying mesoscopic information. Fluctuations remain finite and well defined. Connections with usual quantum-field-theory limit enables us to evaluate χ_c ~ 1.007110. Equivalently, for a mesoscopic parallel-plate capacitor, the shot noise distribution becomes operative with χ_c ~ 0.94705 as well being related to the density of virtual pairs. Temperature decoherence and capacitor control are discussed by considering typical values of quantum dot devices and Coulomb blockade theory.

Dispersive switching effect is examined for a mesoscopic system of coherently injected two-level Rydberg atoms into a driven single-mode superconducting cavity. The effect concerns the switching of the output field by simultaneously varying the atomic and cavity detuning parameters at fixed values of the coherent driving field. For certain atomic coherence parameters, symmetric and asymmetric switching diagrams are exhibited, which include one- and two-way process via multistep transitions between output field states.

Shape phase transitions in nuclei, an example of quantum phase transitions in mesoscopic systems, are briefly reviewed. Spectral signatures of critical points in finite quantal systems are discussed and experimental examples are shown.

Electrical noise produced when charges flow through a mesoscopic conductor is non-Gaussian, where higher order cumulants carry valuable information about the microscopic transport process. In these notes we briefly discuss the experimental situation and show that theoretical descriptions for the detection of electrical noise with Josephson junctions lead to generalizations of classical and quantum theories, respectively, for decay rates out of metastable states.

This paper reviews the method of bosonization for one-dimensional interacting fermions. Example of its application to mesoscopic systems is presented with an explicit calculation of the spin and charge currents in an interacting quantum wire subject to a uniform magnetic field and alternating voltage source. Special emphasis is given to the details of the calculation using bosonization and Keldysh techniques.