Calculations of canonical averages from the grand canonical ensemble

Grand canonical and canonical ensembles become equivalent in the thermodynamic limit, but when the system size is finite the results obtained in the two ensembles deviate from each other. In many important cases, the canonical ensemble provides an appropriate physical description but it is often much easier to perform the calculations in the corresponding grand canonical ensemble. We present a method to compute averages in canonical ensemble based on calculations of the expectation values in grand canonical ensemble. The number of particles, which is fixed in the canonical ensemble, is not necessarily the same as the average number of particles in the grand canonical ensemble

Population of isomers in decay of the giant dipole resonance

The value of an isomeric ratio (IR) in N=81 isotones ($^{137}$Ba, $^{139}$Ce, $^{141}$Nd and $^{143}$Sm) is studied by means of the ($\gamma, n)$ reaction. This quantity measures a probability to populate the isomeric state in respect to the ground state population. In ($\gamma, n)$ reactions, the giant dipole resonance (GDR) is excited and after its decay by a neutron emission, the nucleus has an excitation energy of a few MeV. The forthcoming $\gamma$ decay by direct or cascade transitions deexcites the nucleus into an isomeric or ground state. It has been observed experimentally that the IR for $^{137}$Ba and $^{139}$Ce equals about 0.13 while in two heavier isotones it is even less than half the size. To explain this effect, the structure of the excited states in the energy region up to 6.5 MeV has been calculated within the Quasiparticle Phonon Model. Many states are found connected to the ground and isomeric states by $E1$, $E2$ and $M1$ transitions. The single-particle component of the wave function is responsible for the large values of the transitions. The calculated value of the isomeric ratio is in very good agreement with the experimental data for all isotones. A slightly different value of maximum energy with which the nuclei rest after neutron decay of the GDR is responsible for the reported effect of the A-dependence of the IR.Comment: 16 pages, 4 Fig

Spin splitting of X-related donor impurity states in an AlAs barrier

We use magnetotunneling spectroscopy to observe the spin splitting of the ground state of an X-valley-related Si-donor impurity in an AlAs barrier. We determine the absolute magnitude of the effective Zeeman spin splitting factors of the impurity ground state to be g$_{I}$= 2.2 $\pm$ 0.1. We also investigate the spatial form of the electron wave function of the donor ground state, which is anisotropic in the growth plane

An ab initio theory of double odd-even mass differences in nuclei

Two aspects of the problem of evaluating double odd-even mass differences D_2 in semi-magic nuclei are studied related to existence of two components with different properties, a superfluid nuclear subsystem and a non-superfluid one. For the superfluid subsystem, the difference D_2 is approximately equal to 2\Delta, the gap \Delta being the solution of the gap equation. For the non-superfluid subsystem, D_2 is found by solving the equation for two-particle Green function for normal systems. Both equations under consideration contain the same effective pairing interaction. For the latter, the semi-microscopic model is used in which the main term calculated from the first principles is supplemented with a small phenomenological addendum containing one phenomenological parameter supposed to be universal for all medium and heavy atomic nuclei.Comment: 7 pages, 10 figures, Report at Nuclear Structure and Related Topics, Dubna, Russia, July 2 - July 7, 201

Partial level density of the n-quasiparticle excitations in the nuclei of the 39< A <201 region

Level density and radiative strength functions are obtained from the analysis of two-step cascades intensities following the thermal neutrons capture. The data on level density are approximated by the sum of the partial level densities corresponding to n quasiparticles excitation. The most probable values of the collective enhancement factor of the level density are found together with the thresholds of the next Cooper nucleons pair breaking. These data allow one to calculate the level density of practically any nucleus in given spin window in the framework of model concepts, taking into account all known nuclear excitation types. The presence of an approximation results discrepancy with theoretical statements specifies the necessity of rather essentially developing the level density models. It also indicates the possibilities to obtain the essentially new information on nucleon correlation functions of the excited nucleus from the experiment.Comment: 29 pages, 8 figures, 2 table

Nonlinear electron transport in normally pinched-off quantum wire

Nonlinear electron transport in normally pinched-off quantum wires was studied. The wires were fabricated from AlGaAs/GaAs heterostructures with high-mobility two-dimensional electron gas by electron beam lithography and following wet etching. At certain critical source-drain voltage the samples exhibited a step rise of the conductance. The differential conductance of the open wires was noticeably lower than e^2/h as far as only part of the source-drain voltage dropped between source contact and saddle-point of the potential relief along the wire. The latter limited the electron flow injected to the wire. At high enough source-drain voltages the decrease of the differential conductance due to the real space transfer of electrons from the wire in GaAs to the doped AlGaAs layer was found. In this regime the sign of differential magnetoconductance was changed with reversing the direction of the current in the wire or the magnetic field, whet the magnetic field lies in the heterostructure plane and is directed perpendicular to the current. The dependence of the differential conductance on the magnetic field and its direction indicated that the real space transfer events were mainly mediated by the interface scattering.Comment: LaTeX 2e (epl.cls) 6 pages, 3 figure

Wave function mapping conditions in Open Quantum Dots structures

We discuss the minimal conditions for wave function spectroscopy, in which resonant tunneling is the measurement tool. Two systems are addressed: resonant tunneling diodes, as a toy model, and open quantum dots. The toy model is used to analyze the crucial tunning between the necessary resolution in current-voltage characteristics and the breakdown of the wave functions probing potentials into a level splitting characteristic of double quantum wells. The present results establish a parameter region where the wavefunction spectroscopy by resonant tunneling could be achieved. In the case of open quantum dots, a breakdown of the mapping condition is related to a change into a double quantum dot structure induced by the local probing potential. The analogy between the toy model and open quantum dots show that a precise control over shape and extention of the potential probes is irrelevant for wave function mapping. Moreover, the present system is a realization of a tunable Fano system in the wave function mapping regime.Comment: 6 pages, 6 figure

Abelian symmetries in multi-Higgs-doublet models

N-Higgs doublet models (NHDM) are a popular framework to construct electroweak symmetry breaking mechanisms beyond the Standard model. Usually, one builds an NHDM scalar sector which is invariant under a certain symmetry group. Although several such groups have been used, no general analysis of symmetries possible in the NHDM scalar sector exists. Here, we make the first step towards this goal by classifying the elementary building blocks, namely the abelian symmetry groups, with a special emphasis on finite groups. We describe a strategy that identifies all abelian groups which are realizable as symmetry groups of the NHDM Higgs potential. We consider both the groups of Higgs-family transformations only and the groups which also contain generalized CP transformations. We illustrate this strategy with the examples of 3HDM and 4HDM and prove several statements for arbitrary N.Comment: 33 pages, 2 figures; v2: conjecture 3 is proved and becomes theorem 3, more explanations of the main strategy are added, matches the published versio

Chaotic oscillations in a map-based model of neural activity

We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find condition under which this map has an invariant region on the phase plane, containing chaotic attractor. This attractor creates chaotic spiking-bursting oscillations of the model. We also show various regimes of other neural activities (subthreshold oscillations, phasic spiking etc.) derived from the proposed model

A magnetically-induced Coulomb gap in graphene due to electron-electron interactions

Insights into the fundamental properties of graphene's Dirac-Weyl fermions have emerged from studies of electron tunnelling transistors in which an atomically thin layer of hexagonal boron nitride (hBN) is sandwiched between two layers of high purity graphene. Here, we show that when a single defect is present within the hBN tunnel barrier, it can inject electrons into the graphene layers and its sharply defined energy level acts as a high resolution spectroscopic probe of electron-electron interactions in graphene. We report a magnetic field dependent suppression of the tunnel current flowing through a single defect below temperatures of $\sim$ 2 K. This is attributed to the formation of a magnetically-induced Coulomb gap in the spectral density of electrons tunnelling into graphene due to electron-electron interactions