On the superfluidity of classical liquid in nanotubes

In 2001, the author proposed the ultra second quantization method. The ultra second quantization of the Schr\"odinger equation, as well as its ordinary second quantization, is a representation of the N-particle Schr\"odinger equation, and this means that basically the ultra second quantization of the equation is the same as the original N-particle equation: they coincide in 3N-dimensional space. We consider a short action pairwise potential V(x_i -x_j). This means that as the number of particles tends to infinity, $N\to\infty$, interaction is possible for only a finite number of particles. Therefore, the potential depends on N in the following way: $V_N=V((x_i-x_j)N^{1/3})$. If V(y) is finite with support $\Omega_V$, then as $N\to\infty$ the support engulfs a finite number of particles, and this number does not depend on N. As a result, it turns out that the superfluidity occurs for velocities less than $\min(\lambda_{\text{crit}}, \frac{h}{2mR})$, where $\lambda_{\text{crit}}$ is the critical Landau velocity and R is the radius of the nanotube.Comment: Latex, 20p. The text is presented for the International Workshop "Idempotent and tropical mathematics and problems of mathematical physics", Independent University of Moscow, Moscow, August 25--30, 2007 and to be published in the Russian Journal of Mathematical Physics, 2007, vol. 15, #

Probability Theory Compatible with the New Conception of Modern Thermodynamics. Economics and Crisis of Debts

We show that G\"odel's negative results concerning arithmetic, which date back to the 1930s, and the ancient "sand pile" paradox (known also as "sorites paradox") pose the questions of the use of fuzzy sets and of the effect of a measuring device on the experiment. The consideration of these facts led, in thermodynamics, to a new one-parameter family of ideal gases. In turn, this leads to a new approach to probability theory (including the new notion of independent events). As applied to economics, this gives the correction, based on Friedman's rule, to Irving Fisher's "Main Law of Economics" and enables us to consider the theory of debt crisis.Comment: 48p., 14 figs., 82 refs.; more precise mathematical explanations are added. arXiv admin note: significant text overlap with arXiv:1111.610

Nonlinear dynamics of soft fermion excitations in hot QCD plasma III: Soft-quark bremsstrahlung and energy losses

In general line with our early works [Yu.A. Markov, M.A. Markova, Nucl. Phys. A770 (2006) 162; 784 (2007) 443] within the framework of a semiclassical approximation the general theory of calculation of effective currents and sources generating bremsstrahlung of an arbitrary number of soft quarks and soft gluons at collision of a high-energy color-charged particle with thermal partons in a hot quark-gluon plasma, is developed. For the case of one- and two-scattering thermal partons with radiation of one or two soft excitations, the effective currents and sources are calculated in an explicit form. In the model case of `frozen' medium, approximate expressions for energy losses induced by the most simple processes of bremsstrahlung of soft quark and soft gluon, are derived. On the basis of a conception of the mutual cancellation of singularities in the sum of so-called `diagonal' and `off-diagonal' contributions to the energy losses, an effective method of determining color factors in scattering probabilities, containing the initial values of Grassmann color charges, is suggested. The dynamical equations for Grassmann color charges of hard particle used by us early are proved to be insufficient for investigation of the higher radiative processes. It is shown that for correct description of these processes the given equations should be supplemented successively with the higher-order terms in powers of the soft fermionic field.Comment: 93 pages, 20 figure

Mathematical Conception of "Phenomenological" Equilibrium Thermodynamics

In the paper, the principal aspects of the mathematical theory of equilibrium thermodynamics are distinguished. It is proved that the points of degeneration of a Bose gas of fractal dimension in the momentum space coincide with critical points or real gases, whereas the jumps of critical indices and the Maxwell rule are related to the tunnel generalization of thermodynamics. Semiclassical methods are considered for the tunnel generalization of thermodynamics and also for the second and ultrasecond quantization (operators of creation and annihilation of pairs). To every pure gas there corresponds a new critical point of the limit negative pressure below which the liquid passes to a dispersed state (a foam). Relations for critical points of a homogeneous mixture of pure gases are given in dependence on the concentration of gases.Comment: 37 pages, 9 figure, more precise explanations, more references. arXiv admin note: substantial text overlap with arXiv:1202.525

Probability of Pulse Overlap as a Quantitative Indicator of Signal Environment Complexity

Introduction. Simultaneous operation of numerous sources of radio emission form complex signal environment. Different devices with the common name “wideband analyzers” (WBA) are widely used to analyze and to control such environment. There is currently a need for developing the quantitative characteristics of a complex signal environment, which will make it possible to predict the stability of the WBA operation.Aim. The development of the indicator of the signal environment complexity, which will make possible the quantitative assessment of such environment.Materials and methods. To provide the desired indicator, simulation and mathematical tools for random events description are used. All calculations are performed using MatLab.Results. The principles of disturbances in the WBA receiver and algorithmic errors in the processing of overlapped signals are described. To quantify the “complexity” of the signal environment it is proposed to use the probability that pulses from several sources overlap in time. This allows one to compare signal environments with each other. The new analytical expression for estimating the pulse overlap probability is proposed. Functions of the pulse overlap probability from the complex signal environment parameters were obtained.Conclusion. According to the comparative analysis of the calculations using proposed analytical expression and simulation, the new expression allows one to achieve the calculation speed up to 6 orders of magnitude higher with an error below 7% compared to the simulation. The high performance of the calculations using the proposed expression allows one to simulate the complex signal environment in dynamics more efficiently.Introduction. Simultaneous operation of numerous sources of radio emission form complex signal environment. Different devices with the common name “wideband analyzers” (WBA) are widely used to analyze and to control such environment. There is currently a need for developing the quantitative characteristics of a complex signal environment, which will make it possible to predict the stability of the WBA operation.Aim. The development of the indicator of the signal environment complexity, which will make possible the quantitative assessment of such environment.Materials and methods. To provide the desired indicator, simulation and mathematical tools for random events description are used. All calculations are performed using MatLab.Results. The principles of disturbances in the WBA receiver and algorithmic errors in the processing of overlapped signals are described. To quantify the “complexity” of the signal environment it is proposed to use the probability that pulses from several sources overlap in time. This allows one to compare signal environments with each other. The new analytical expression for estimating the pulse overlap probability is proposed. Functions of the pulse overlap probability from the complex signal environment parameters were obtained.Conclusion. According to the comparative analysis of the calculations using proposed analytical expression and simulation, the new expression allows one to achieve the calculation speed up to 6 orders of magnitude higher with an error below 7% compared to the simulation. The high performance of the calculations using the proposed expression allows one to simulate the complex signal environment in dynamics more efficiently

Conductance of a Mott Quantum Wire

We consider transport through a one-dimensional conductor subject to an external periodic potential and connected to non-interacting leads (a "Mott quantum wire"). For the case of a strong periodic potential, the conductance is shown to jump from zero, for the chemical potential lying within the Mott-Hubbard gap, to the non-interacting value of 2e^2/h, as soon as the chemical potential crosses the gap edge. This behavior is strikingly different from that of an optical conductivity, which varies continuously with the carrier concentration. For the case of a weak potential, the perturbative correction to the conductance due to Umklapp scattering is absent away from half-filling.Comment: 4 pages, RevTex, 1 ps figure included; published versio

Initial Conditions for Semiclassical Field Theory

Semiclassical approximation based on extracting a c-number classical component from quantum field is widely used in the quantum field theory. Semiclassical states are considered then as Gaussian wave packets in the functional Schrodinger representation and as Gaussian vectors in the Fock representation. We consider the problem of divergences and renormalization in the semiclassical field theory in the Hamiltonian formulation. Although divergences in quantum field theory are usually associated with loop Feynman graphs, divergences in the Hamiltonian approach may arise even at the tree level. For example, formally calculated probability of pair creation in the leading order of the semiclassical expansion may be divergent. This observation was interpretted as an argumentation for considering non-unitary evolution transformations, as well as non-equivalent representations of canonical commutation relations at different time moments. However, we show that this difficulty can be overcomed without the assumption about non-unitary evolution. We consider first the Schrodinger equation for the regularized field theory with ultraviolet and infrared cutoffs. We study the problem of making a limit to the local theory. To consider such a limit, one should impose not only the requirement on the counterterms entering to the quantum Hamiltonian but also the requirement on the initial state in the theory with cutoffs. We find such a requirement in the leading order of the semiclassical expansion and show that it is invariant under time evolution. This requirement is also presented as a condition on the quadratic form entering to the Gaussian state.Comment: 20 pages, Plain TeX, one postscript figur

Berry phase in graphene: a semiclassical perspective

We derive a semiclassical expression for the Green's function in graphene, in which the presence of a semiclassical phase is made apparent. The relationship between this semiclassical phase and the adiabatic Berry phase, usually referred to in this context, is discussed. These phases coincide for the perfectly linear Dirac dispersion relation. They differ however when a gap is opened at the Dirac point. We furthermore present several applications of our semiclassical formalism. In particular we provide, for various configurations, a semiclassical derivation of the electron's Landau levels, illustrating the role of the semiclassical ``Berry-like'' phas