abstract

Rocking ratchets are asymmetric potentials operated in the non-linear response regime where rectifying behaviour can be observed. Mesoscopic electronic devices based on semiconductors with low carrier concentration are easily driven away from linear response, and their electron dynamics is at low temperatures altered by quantum effects. Asymmetric semiconductor devices of sub-micron dimensions are therefore suitable for experiments on “quantum ratchets”, that is, rocking ratchets based on quantum effects, such as electron interference and tunnelling. We first describe experiments using triangular electron cavities in the linear response regime, illustrating that, at low temperatures, classical and quantum electron dynamics are determined by the shape of the ballistic cavity. Physical reasons for a transition from linear to non-linear behaviour in mesoscopic devices are discussed, and two ratchet experiments in the non-linear regime are described. The sign of rectification in a quantum dot ratchet, based on electron interference effects, depends very sensitively on uncontrollably small deviations from the intended device shape, but can be tuned using parameters such as magnetic field, Fermi energy or the AC voltage. The current direction in a tunneling ratchet can be predicted from the device shape, and is tunable by temperature, when device parameters are suitably chosen.

abstract

Motor proteins are individual molecules that hydrolyze ATP and use the released energy to move forward along a polymer. These microscopic engines operate in an overdamped regime where Brownian motion is a nonegligible contribution to the physics. We provide a new definition for the efficiency of an engine in the overdamped Brownian realm and discuss how a high efficiency can be reached.

abstract

We investigate a new approach which has been recently introduced to construct microscopic engines whose main characteristic is the possibility to determine dynamically the direction of motion. The approach is based on the transformation of the supplied energy into directed motion through a dynamical competition between the intrinsic lengths of the moving object and the substrate. The engines are able to move translationally or rotationally and can perform useful functions such as pulling of a cargo. We discuss possible realizations and introduce some ingredients, such as turns and switches, important for creating a microscopic ‘railway system.’

abstract

The problem of the classical deterministic dynamics of a particle in a periodic asymmetric potential of the ratchet type is addressed. When the inertial term is taken into account, the dynamics can be chaotic and modify the transport properties. By a comparison between the bifurcation diagram and the current, we identify the origin of the current reversal as a bifurcation from a chaotic to a periodic regime. Close to this bifurcation, we observed trajectories revealing intermittent chaos and anomalous deterministic diffusion. We extend our previous analysis of this problem to include multiple current reversal and the orbits in phase space.

abstract

Overdamped directed motion of Brownian motors in a spatially periodic system, induced by Poissonian fluctuations of various statistics and driven by thermal noise, is investigated. Two models of asymmetric as well as two models of symmetric Poissonian fluctuations are considered. Transport properties in dependence upon statistics of fluctuations imposed on the system are analyzed.

abstract

The diffusion of a Brownian particle in a continuum subject to external potential forces as well as nonhomogeneous thermal field is discussed. Apart from a thermodiffusion phenomenon, a Streater effect in which the potential energy of the particle is converted to a heat due to friction cf. R.F. Streater, Rep. Math. Phys. 40, 557 (1997), is taken into account. It is shown that for such a continuum the first law of thermodynamics holds true, and the second law is observed if a relation between the probability density function and temperature is satisfied. The examples of the Brownian motion for particular external fields are given.

abstract

The effective method of simulation of stochastic excitable media by en ensemble of Brownian particles is presented. The system studied is a variant of Rinzel–Keller model with global inhibition. The formation, time evolution, and statistical properties of localized structures — spots — are investigated.

abstract

Kramers turnover theory is solved for a particle in a symmetric triple well potential for temperatures above the crossover temperature between tunneling and activated barrier crossing. Comparison with the turnover theory for a double well potential shows that the presence of the intermediate well always leads to a decrease of the reaction rate. At most though, the rate is a factor of two smaller than in the case of a double well potential.

abstract

Diffusion in a one-dimensional system with a thin membrane (which is treated as a partially permeable wall) for the discrete and continuous time and space variables is discussed. The internal structure of the membrane is not explicitly involved into consideration. Starting from microscopic models of diffusion we obtain the boundary condition at the membrane for macroscopic diffusion equation.

abstract

A Modified Alloy Analogy (MAA) for the single-band Hubbard model is used to investigate the interplay of ferromagnetic order and electrical conductivity in a system of itinerant band electrons. The alloy analogy is evaluated within the framework of the Coherent Potential Approximation (CPA). The tensor conductivity, normally a two-particle Green function, can be represented by single-particle terms if CPA-consistent approaches are applied [B.Velický, Phys. Rev. 184, 614 (1969)]. The MAA is used for fcc and bcc lattices. Spontaneous ferromagnetism appears in the fcc lattice for a more than half-filled energy band (\(1\lt \!n\!\lt 2\)). In the bcc lattice collective order is restricted to a small \(n\)-region. The electrical conductivity is investigated for different Coulomb strengths \(U\) as function of band occupation \(n\) and temperature \(T\). The conductivity turns out to be substantially higher in the ferromagnetic than in the paramagnetic phase, even diverging in the case of ferromagnetic saturation (\(T\rightarrow 0\)), where electron–electron scattering is excluded. Majority-spin carriers contribute the main part to the current in the ferromagnetic phase. The electrical resistivity exhibits a power-like low-temperature behavior becoming critical at \(T_{\rm C}\). Formal similarity to the spin disorder resistivity of local moment systems is observed.

abstract

We analyze the doping dependence of the thermopower and conductivity of ropes of single wall carbon nanotubes using a tight binding model. A sizeable value of the Seebeck coefficient in these systems together with its Fermi liquid like temperature behavior indicate an asymmetry near the Fermi surface. We discuss two possible explanations for this asymmetry of the electronic structure of the nanotube ropes, one due to defect states, another resulting from the intertube interactions.

abstract

Mesoscopic metal rings can carry persistent currents driven by a constant magnetic field. The geometrical structure of a toroidal carbon nanotube can be characterized by four independent parameters. We derive the formula for persistent currents driven by a constant Bohm–Aharonov type of field perpendicular to the plane of the torus. The dependencies of the currents on the chirality, twist and circumference of the torus are discussed.

abstract

We study linear electron transport through a molecular wire sandwiched between nanotube leads. We show that the presence of such electrodes strongly influences the calculated conductance. We find that depending on the quality and geometry of the contacts between the molecule and the tubular reservoirs, linear transport can be tuned between an effective Newns spectral behavior and a more structured one. The latter strongly depends on the topology of the leads. We also provide analytical evidence for an anomalous behavior of the conductance as a function of the contact strength.

abstract

We systematically study the electrical transport through atomic sodium wires connected to two semi-infinite electrodes. The dependence of the resistance on the wire length and on the wire–electrode separation is investigated. For small wire–electrode distances the single sodium atom can show a larger resistance than the Na-dimer, confirming recent ab initio calculations [N.D. Lang, Phys. Rev. Lett. 79, 1357 (1997)]. In our density functional theory based Landauer approach, this anomalous behaviour is shown to be dependent on the level of description of the wire (number of basis functions per atom) as well as on the strength of the electrode–wire coupling.

abstract

We calculate and discuss orbital magnetic susceptibilities in mesoscopic cylinders made of a normal metal or a semiconductor for different shapes of the Fermi surfaces and for different circumferences of the cylinders.

abstract

Quantum percolation problem on 3D simple cubic lattice under influence of external magnetic field is discussed. Results of numerical simulations of magnetoconductance and its dependence on both the system size (temperature) and the concentration of metallic component \(p\) are presented. Qualitative agreement with theory for metals is obtained for large \(p\), when the system is delocalized. For small \(p\), when the system is localized, the agreement with weak localization theory predictions is successfully verified as well.

abstract

In the paper we use numerical simulations to show that superlocalization of electronic wave functions takes place on fractal objects also for energies \(E \) from the band. Finite size scaling of conductance \(g\) versus system size \(L \) reveals that \(\langle \ln g\rangle \) scales as \(L^{d_{\phi }}\). The values of localization exponent \(d_{\phi }\) we found in 2D are \(1.138(3)\) for the state in the middle of the band \(E=0.5t\), and \(1.144(3)\) for the state near the lower band edge \(E=-3.5t.\) These values are in good agreement with the conjecture \(d_{\phi }=\zeta _{l}\), where \(\zeta _{l}\) is the chemical length exponent.

abstract

In this article we present the results of our investigations on the ground and the first excited states of a polaron in a polar semiconductor quantum dot in both two and three dimensions. We have also discussed the stability of a strong-coupling bipolaron in quantum dots. We have shown that below a critical value of the confinement length the bipolaron becomes unstable in a quantum dot and breaks up into two individual polarons. We have finally shown that the phonon-induced Zeeman splitting of the first excited level of a two-dimensional parabolic quantum dot becomes strongly size dependent below a certain size and decreases very rapidly with decreasing dot size.

abstract

In the article a simplified version of the Hartree method is proposed for calculation of electron states in a quantum dot. The results obtained by the use of the standard and the simplified Hartree methods are compared. Total energy of electrons confined in the quantum well allows to estimate capacitance of the dot.

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When all 3 dimensions of electron device drop to a nanometer size, a 0-D device or a quantum dot appears. In this case the conductance shows oscillations with varying gate voltage. In this paper the results of numerical simulations, which clearly show the above behavior, are presented. The dot conductance is calculated with the help of Landauer formula after the Green’s function corresponding to device Hamiltonian is evaluated. Coulomb interactions are included as the Hartree potential associated with the charge of all particles inside a dot. This forces us to use self-energies which describes interactions between device and leads not only to propagating states but also to non-propagating, localized states below the band.

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We review some recently performed experiments concerning the detection of phase transitions in solids with the use of a single measurement of the chemical potential versus temperature. A new method of the indirect measurement of the chemical potential was demonstrated for Gd, Gd\(_5\)Si\(_4\), Cr, TiNi (10% and 15% of deformation) and CuAlNiTiMn samples by means of a simple electrochemical experiment. For most cases the method allowed easily to detect all critical temperatures \(T_{\mathrm {C}}\) (Gd, Gd\(_5\)Si\(_4\)), \(T_{\mathrm {N}}\) (Cr) and the structural transition temperatures (TiNi, CuAlNiTiMn). The obtained results were in the exceptionally good agreement with other measurements and entirely supported the theoretical predictions concerning the applicability of the method. Presumably, it is also possible to detect phase transition anomalies, using the method of chemical potential measurement, either by thermoelectric or photoelectric effects.

abstract

We study the problem of the upper critical field (\(H_{\rm c2}\)) for tight-binding electrons in a phase with stripes. Carrying out calculations for finite systems we analyze the influence of the external field in the commensurable and incommensurable case on an equal footing. The upper critical field is discussed for anisotropic intersite pairing as a function of the width of stripe. We show that the upper critical field increases with a decrease of the width of stripe. This effect is of particular importance close to the superconducting transition temperature.

abstract

The electronic structure of Fe\(_{3-x}\)V\(_{x}\)M (M=Al, Ga) alloys was investigated by ab initio method. Magnetic and non-magnetic band structure of Fe\(_{3-x}\)V\(_{x}\)M was calculated for concentrations \(x=0.0\)–1.0. Calculations have shown that the transition from magnetic to non-magnetic state is accompanied by the qualitative changes in the band structure in the vicinity of the Fermi level (\(\varepsilon _{\rm F}\)). For concentrations \(0.5\le x\le 1\) the Density Of States (DOS) at \(\varepsilon _{\rm F}\) in both magnetic states display a sharp peak composed solely of the \(3d\) states of impurity Fe-AS atom ( Fe atom at nominally V atom position of Fe\(_{2}\)VAl Heusler compound). In the magnetic state only majority-spin states enter the DOS near \(\varepsilon _{\rm F}\). The quasi-gap around the \(\varepsilon _{\rm F}\) found in Fe\(_{2}\)VM is filled up by 3d\(\uparrow \) states of Fe-AS which produce the sharp structures at \(\varepsilon _{\rm F}\). Transition to the non-magnetic state results in the narrowing and strengthening of the peak of Fe-AS 3d-states DOS at \(\varepsilon _{\rm F}\) and the opening of the well-defined gap just above the Fermi level. The changes of the DOS around \(\varepsilon _{\rm F}\) connected with the variation of Fe-AS concentration and magnetic transition explain the peculiar behavior of the electrical resistivity observed experimentally.

abstract

We study the influence of a strong magnetic field on a superconducting state of electron gas in a two-dimensional square lattice. The Harper equation is extended in order to include pairing interactions between electrons. We examine the effects of superconductivity with different pairing symmetries on the Hofstadter energy spectra.

abstract

We have considered phonon-induced superconductivity in the presence of the pseudogap originating from Charge–Density–Wave (CDW) excitations within the two-dimensional lattice. Eliashberg formalism has been applied and the CDW effects have been taken into account with the help of the renormalization of propagators in the Dyson equation. The CDW gap has been incorporated in the semiphenomenological way, assuming the \(d\)-wave symmetry. We have evaluated the superconducting transition temperature \(T_{\rm c}\) as a function of doping. The influence of the normal-state pseudogap on the isotope shift exponent has also been considered.

abstract

In the paper we show that for detailed treatment of small devices by the Green’s function technique the self-energies due to the leads should be considered for both extended and localized states.

abstract

The coupled states of two kinks and/or antikinks for scalar model with fourth-order potential in presence of linear and nonlinear frictional terms and absence of external force are constructed.

abstract

We explain in this paper in simple terms the behavior of two-photon lasers and describe recent results that have led to the realization of the first continuous-wave two-photon optical laser. We stress the differences between one- and two-photon lasers to develop an appreciation of their dynamics and the difficulties associated with achieving two-photon lasing. We find similarities and significant differences between the one- and two-photon polarizations of the medium, population inversion and mode-pulling formula. The theory is treated semiclassically by using Maxwell–Bloch equations. We study the linear stability analysis of the steady state of the system which is taken to be contained in a ring cavity. The results are illustrated with an application to a specific atomic system in a long sample of sodium vapor as an amplifying medium, in which the possibility of short pulse train generation is exhibited.

abstract

Kinetics of three-dimensional normal grain growth and related processes (e.g., soap froth evolutions) described by the Mulheran–Harding model is studied. The model is represented by a diffusion equation with the grain–size–dependent diffusion coefficient. The equation is solved for an arbitrary initial distribution of grain sizes. It is proved that asymptotic kinetics do not depend on the initial state.

abstract

We propose a new method of valuation of portfolios and their respective investing strategies. To this end we define a canonical ensemble of portfolios that allows to use the formalism of thermodynamics.