scholarly journals PARITY VIOLATION AND THE MEAN FIELD APPROXIMATION FOR THE ANYON GAS

1993 ◽  
Vol 08 (20) ◽  
pp. 1909-1915 ◽  
Author(s):  
DIDIER CAENEPEEL ◽  
RICHARD MACKENZIE
Keyword(s):  
Magnetic Field ◽  
Parity Violation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Radius Of Curvature ◽  
Interparticle Separation ◽  
The Mean ◽  
The One ◽  
Self Consistency

We examine an approach to justifying the mean field approximation for the anyon gas, using the scattering of anyons. Parity violation permits a nonzero average scattering angle, from which one can extract a mean radius of curvature for anyons. If this is larger than the interparticle separation, one expects that the graininess of the statistical magnetic field is unimportant, and that the mean field approximation is good. We argue that a non-conventional interaction between anyons is crucial, in which case the criterion for validity of the approximation is identical to the one deduced using a self-consistency argument.

scholarly journals The Combined Effect of Rotation and Magnetic Field on Finite-Amplitude Thermal Convection

1973 ◽  
Vol 26 (5) ◽  
pp. 617 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Finite Amplitude ◽  
Combined Effect ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Wide Range ◽  
The Mean ◽  
Basic Equations

The combined effect of an imposed rotation and magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. The basic equations are derived by a variational technique and their solutions are then found over a wide range of conditions, in the case of free boundaries, by numerical and analytic techniques, in particular by asymptotic and perturbation methods. The results obtained by the different techniques are shown to be in excellent agreement. As for the linear theory, the calculations predict that the simultaneous presence' of a magnetic field and rotation may produce conflicting tendencies.

The Glauber and Metropolis Transition Rates on the Stationary States of the Ising Model

1997 ◽  
Vol 11 (13) ◽  
pp. 565-570
Author(s):  
G. L. S. Paula ◽  
W. Figueiredo
Keyword(s):  
Ising Model ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Two Dimensions ◽  
Mean Field Approximation ◽  
Stationary States ◽  
Transition Rates ◽  
The Mean ◽  
The One

We have applied the Glauber and Metropolis prescriptions to investigate the stationary states of the Ising model in one and two dimensions. We have employed the formalism of the master equation to follow the evolution of the system towards the stationary states. Although the Glauber and Metropolis transition rates lead the system to the same equilibrium states for the Ising model in the Monte Carlo simulations, we show that they can predict different results if we disregard the correlations between spins. The critical temperature of the one-dimensional Ising model cannot even be found by using the Metropolis algorithm and the mean field approximation. However, taking into account only correlations between nearest neighbor spins, the resulting stationary states become identical for both Glauber and Metropolis transition rates.

scholarly journals Parity violation, anyon scattering, and the mean field approximation

1994 ◽  
Vol 50 (8) ◽  
pp. 5418-5424 ◽  
Author(s):  
Didier Caenepeel ◽  
Richard MacKenzie
Keyword(s):  
Parity Violation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
The Mean

scholarly journals On Magnetic Inhibition of Thermal Convection

1972 ◽  
Vol 25 (6) ◽  
pp. 703 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy ◽  
EA Spiegel
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Quantitative Estimates ◽  
Wide Range ◽  
The Face ◽  
The Mean ◽  
The Magnetic Field

The effect of an imposed vertical magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. Solutions are found over a wide range of conditions, for free boundaries, by a combination of numerical and analytic techniques. Quantitative estimates are made of the significant modifications to the heat transfer which are brought about by the presence of the magnetic field. It is found that the general properties of nonlinear steady cellular convection seem to persist in the face of magnetic inhibition.

scholarly journals WRITING ELECTRONIC FERROMAGNETIC STATES IN A HIGH-TEMPERATURE PARAMAGNETIC NUCLEAR SPIN SYSTEM

2011 ◽  
Vol 09 (04) ◽  
pp. 1047-1056 ◽  
Author(s):  
D. O. SOARES-PINTO ◽  
J. TELES ◽  
A. M. SOUZA ◽  
E. R. DEAZEVEDO ◽  
R. S. SARTHOUR ◽  
...  
Keyword(s):  
Magnetic Field ◽  
High Temperature ◽  
Mean Field ◽  
Field Approximation ◽  
Order Transition ◽  
Mean Field Approximation ◽  
Temperature Hysteresis ◽  
First Case ◽  
The Matrix ◽  
The Mean

In this paper, we use Nuclear Magnetic Resonance (NMR) to write electronic states of a ferromagnetic system into high-temperature paramagnetic nuclear spins. Through the control of phase and duration of radio frequency pulses, we set the NMR density matrix populations, and apply the technique of quantum state tomography to experimentally obtain the matrix elements of the system, from which we calculate the temperature dependence of magnetization for different magnetic fields. The effects of the variation of temperature and magnetic field over the populations can be mapped in the angles of spin rotations, carried out by the RF pulses. The experimental results are compared to the Brillouin functions of ferromagnetic ordered systems in the mean field approximation for two cases: the mean field is given by (i) B = B0 + λM and (ii) B = B0 + λM + λ′M3, where B0 is the external magnetic field, and λ, λ′ are mean field parameters. The first case exhibits second order transition, whereas the second case has first order transition with temperature hysteresis. The NMR simulations are in good agreement with the magnetic predictions.

A TWO-BAND SUPERCONDUCTOR WITH A NARROW BAND NEAR THE FERMI LEVEL

1988 ◽  
Vol 02 (05) ◽  
pp. 679-680
Author(s):  
V. P. Galaiko
Keyword(s):  
Fermi Level ◽  
Narrow Band ◽  
Mean Field ◽  
Wide Band ◽  
Field Approximation ◽  
System Stability ◽  
Mean Field Approximation ◽  
Strong Electron ◽  
The Mean ◽  
The One

The modern theory of conventional superconductivity is based upon the concept of quantum states with broken gauge symmetry providing non-zero values for the so-called "anomalous averages" [Formula: see text], [Formula: see text]. Being applied to the simplest Gorikov-like semiphenomenological electronic scenario for a metal superconductor, this idea (in the mean field approximation) leads towards a complete description of all properties of ordinary superconductors as a manifestation of macroscopic quantum phase coherence. Currently there exists already strong experimental evidence that the newly discovered high Tc superconductors exhibit the same quantum coherence effects including the highly characteristic quantity for these phenomena, namely the doubled electronic charge. On these grounds one can expect that the high Tc superconductors should also be described by "anomalous averages" of the same kind. The only question is whether Gorikov's scenario is still sufficient or we need a new scenario instead in order to grasp the whole situation. In the case of Gorikov's scenario one needs to explain how the strong electron-electron coupling (no matter of what origin) can be consistent with the system stability condition. Yet there is another argument in favour of a new scenario. The large variety of the new SC properties cannot be explained by a model with too limited number of physical parameters. In our dealing with the problem of a possible new scenario we have suggested that in order to understand the high T c superconductors one should not perhaps go so far as to doubt the one-particle approximation and to introduce the Hubbard-like models, RVB and so on. Taking into account the crystalline structure of perfect high T c superconductors we have assumed within the one-particle description the two overlapping bands approach which was proposed by Suhl, Mattias and Walker (USA) and Moskalenko (USSR) as early as in 1959. To obtain qualitatively new results we have suggested a sharp asymmetry between the two bands (one being practically a local energy level close to the Fermi level) and also a special structure of direct electron-electron interaction with dominating interband scattering of singlet electron pairs described by an amplitude g. As the final analysis has shown, an inevitable but comparatively small splitting of the two bands does not invalidate the results of the model. As to the peculiar structure of interaction we believe it might be explained through a strong electron-optical phonon coupling due to the Jahn-Teller-like instability manifested in tetragonal-orthorhombic transitions of HT c samples. The model just outlined can indeed yield high T c . In the mean field approximation (with two superconductivity order parameters) the order of magnitude of T c is given by T c ~ (|g|N(o)/2)2 EF where N(o) is the density of states in the wide band at the Fermi level and EF is a wide band width. There is an exponentially sharp decline of T c while overdoping or underdoping the system and there is also a broad plateau when the narrow band is filled partially (the heavy fermion situation). The other results of calculations including thermodynamics and also kinetic properties for the normal state do not contradict experiments except for the linear temperature dependence of the specific heat observed sometimes. But one must take into account that in reality all high T c superconductors are in fact disordered solutions, and it is necessary to consider the dirty alloy limit with Anderson's theorem being violated because of the narrow band existence. At the same time, as analysis shows, the mean field approximation is not good enough for the model (the small parameter is only ( log 2/|g|N(o))-1) and therefore one has to apply Green's functions technique in order to correct the results. There is also a possibility that the magnetic properties connected with localized spins (if there are any) must be taken into account as well.

Application of the Mean-Field Approximation to the Magnetic and Superconducting Phases of Quasi-One-Dimensional Metal

2009 ◽  
Vol 152-153 ◽  
pp. 591-594 ◽  
Author(s):  
A.V. Rozhkov
Keyword(s):  
Density Wave ◽  
Spin Density Wave ◽  
Mean Field ◽  
Field Approximation ◽  
High Energy ◽  
Mean Field Approximation ◽  
One Dimensional ◽  
Ordered Phases ◽  
The Mean ◽  
The One

We research under what condition the mean-field approximation can be applied to study ordered phases of quasi-one-dimensional metal. It is shown that the mean-field treatment is indeed permissible provided that it is applied not to the microscopic Hamiltonian (subject to severe one-dimensional high-energy fluctuations), but rather to effective Hamiltonian derived at the dimensional crossover scale. The resultant mean-field phase diagram has three ordered phases: spin density wave, charge density wave, and superconductivity. The density wave orders win if the Fermi surface nests well. Outcome of competition between the intra-chain and inter-chain electron repulsion determines the type (spin vs. charge) of the density wave. The ground state becomes superconducting (with unconventional order parameter) when the nesting is poor. The superconducting mechanism relies crucially on the one-dimensional fluctuations.

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