scholarly journals Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic Fields

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1336 ◽  
Author(s):  
Davide Carbone ◽  
Lamberto Rondoni
Keyword(s):  
Magnetic Field ◽  
Statistical Mechanics ◽  
Time Reversal ◽  
Sufficient Conditions ◽  
Reciprocal Relations ◽  
Long Time ◽  
Necessary And Sufficient ◽  
Generalized Time ◽  
The Magnetic Field ◽  
Onsager Reciprocal Relations

Time reversal invariance (TRI) of particles systems has many consequences, among which the celebrated Onsager reciprocal relations, a milestone in Statistical Mechanics dating back to 1931. Because for a long time it was believed that (TRI) dos not hold in presence of a magnetic field, a modification of such relations was proposed by Casimir in 1945. Only in the last decade, the strict traditional notion of reversibility that led to Casimir’s work has been questioned. It was then found that other symmetries can be used, which allow the Onsager reciprocal relations to hold without modification. In this paper we advance this investigation for classical Hamiltonian systems, substantially increasing the number of symmetries that yield TRI in presence of a magnetic field. We first deduce the most general form of a generalized time reversal operation on the phase space of such a system; secondly, we express sufficient conditions on the magnetic field which ensure TRI. Finally, we examine common examples from statistical mechanics and molecular dynamics. Our main result is that TRI holds in a much wider generality than previously believed, partially explaining why no experimental violation of Onsager relations has so far been reported.

scholarly journals Magnetoelastic Nature of Ferromagnetic Shape Memory Effect

2008 ◽  
Vol 583 ◽  
pp. 1-20 ◽  
Author(s):  
Volodymyr A. Chernenko ◽  
Victor A. L'vov
Keyword(s):  
Magnetic Field ◽  
Shape Memory ◽  
Sufficient Conditions ◽  
Alloy System ◽  
Ferromagnetic Shape Memory Alloys ◽  
Fundamental Conception ◽  
Spontaneous Deformation ◽  
Ferromagnetic Shape Memory ◽  
Necessary And Sufficient ◽  
The Magnetic Field

The giant magnetically-induced deformation of ferromagnetic shape memory alloys results from the magnetic field-induced rearrangement of twinned martensite under the magnetic field. This deformation is conventionally referred to as the magnetic-field-induced-strain (MFIS). The MFIS is comparable in value with the spontaneous deformation of crystal lattice during the martensitic transformation of an alloy. Although the first observations of MFIS were reported more than 30 years ago, it has got a world-wide interest 20 years later after the creation of the Ni–Mn–Ga alloy system with its practically important room-temperature martensitic structure and experimental evidence of the large magnetostriction. The underlying physics as well as necessary and sufficient conditions for the observation of MFIS are the main focus of this chapter. A magnetostrictive mechanism of the unusual magnetic and magnetomechanical effects observed in Ni–Mn–Ga alloys is substantiated and a framework of consistent theory of these effects is outlined starting from the fundamental conception of magnetoelasticity and the commonly known principles of ferromagnetism and linear elasticity theories. A reasonable agreement between the theoretical deductions and available experimental data is demonstrated and, in this way, a key role of magnetoelastic coupling in the magnetomechanical behavior of Ni–Mn–Ga alloys is proved. A correspondence of magnetostrictive mechanism to the crystallographic features of MFIS and the basic relationships of the thermodynamics of solids are discussed.

scholarly journals Broadband Linear Polarization in Ap Stars

1993 ◽  
Vol 138 ◽  
pp. 305-309
Author(s):  
Marco Landolfi ◽  
Egidio Landi Degl’Innocenti ◽  
Maurizio Landi Degl’Innocenti ◽  
Jean-Louis Leroy ◽  
Stefano Bagnulo
Keyword(s):  
Magnetic Field ◽  
Circular Polarization ◽  
Linear Polarization ◽  
Rotation Axis ◽  
Spectral Lines ◽  
Line Of Sight ◽  
Long Time ◽  
Rotating Star ◽  
Ap Stars ◽  
The Magnetic Field

AbstractBroadband linear polarization in the spectra of Ap stars is believed to be due to differential saturation between σ and π Zeeman components in spectral lines. This mechanism has been known for a long time to be the main agent of a similar phenomenon observed in sunspots. Since this phenomenon has been carefully calibrated in the solar case, it can be confidently used to deduce the magnetic field of Ap stars.Given the magnetic configuration of a rotating star, it is possible to deduce the broadband polarization at any phase. Calculations performed for the oblique dipole model show that the resulting polarization diagrams are very sensitive to the values of i (the angle between the rotation axis and the line of sight) and β (the angle between the rotation and magnetic axes). The dependence on i and β is such that the four-fold ambiguity typical of the circular polarization observations ((i,β), (β,i), (π-i,π-β), (π-β,π-i)) can be removed.

scholarly journals Magneto-rotatory compressible couple-stress fluid heated from below in porous medium

2016 ◽  
Vol 38 (1) ◽  
pp. 55-63
Author(s):  
Chander Bhan Mehta
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Couple Stress ◽  
Normal Modes ◽  
Sufficient Conditions ◽  
Couple Stress Fluid ◽  
Onset Of Convection ◽  
Medium Permeability ◽  
Effects Of Rotation ◽  
The Magnetic Field

Abstract The study is aimed at analysing thermal convection in a compressible couple stress fluid in a porous medium in the presence of rotation and magnetic field. After linearizing the relevant equations, the perturbation equations are analysed in terms of normal modes. A dispersion relation governing the effects of rotation, magnetic field, couple stress parameter and medium permeability have been examined. For a stationary convection, the rotation postpones the onset of convection in a couple stress fluid heated from below in a porous medium in the presence of a magnetic field. Whereas, the magnetic field and couple stress postpones and hastens the onset of convection in the presence of rotation and the medium permeability hastens and postpones the onset of convection with conditions on Taylor number. Further the oscillatory modes are introduced due to the presence of rotation and the magnetic field which were non-existent in their absence, and hence the principle of exchange stands valid. The sufficient conditions for nonexistence of over stability are also obtained.

scholarly journals Alinement of Solid Interstellar Particles by a Magnetic Field

1965 ◽  
Vol 7 ◽  
pp. 73-76
Author(s):  
Lyman Spitzer ◽  
R. V. Jones
Keyword(s):  
Magnetic Field ◽  
Basic Mechanism ◽  
Thermal Fluctuations ◽  
Solid Particles ◽  
Large Field ◽  
Interstellar Space ◽  
Interstellar Grains ◽  
Long Time ◽  
Satisfactory State ◽  
The Magnetic Field

For a Long Time the Davis-Greenstein Theory (ref. 1) has been generally considered an adequate explanation of the mechanism responsible for the alinement of interstellar grains and thus for the observed interstellar polarization. The magnetic field required to orient paramagnetic grains is apparently somewhat greater than 10-5 gauss, a relatively large field, but according to reference 2 ferromagnetic grains, proposed by the authors of reference 3, can be oriented by a field of only 10-7 gauss. These results indicate that orientation of interstellar grains is easily explained, even if the magnetic field in interstellar space is relatively weak.Unfortunately, this relatively satisfactory state of affairs has been upset by two developments. Firstly, the basic mechanism of magnetic relaxation proposed by Davis and Greenstein has been questioned by Dr. C. Kittel of the University of California, who has pointed out that the disorienting effect associated with thermal fluctuations of magnetization within the solid particles is ignored in the formulation of this mechanism.

scholarly journals Study of the applicability of the curlometer technique with the four Cluster spacecraft in regions close to Earth

2012 ◽  
Vol 30 (3) ◽  
pp. 597-611 ◽  
Author(s):  
S. Grimald ◽  
I. Dandouras ◽  
P. Robert ◽  
E. Lucek
Keyword(s):  
Magnetic Field ◽  
Current Density ◽  
Ring Current ◽  
Current System ◽  
Sufficient Conditions ◽  
Magnetic Activity ◽  
Inner Magnetosphere ◽  
Good Proxy ◽  
The Magnetic Field ◽  
Magnetospheric Current System

Abstract. Knowledge of the inner magnetospheric current system (intensity, boundaries, evolution) is one of the key elements for the understanding of the whole magnetospheric current system. In particular, the calculation of the current density and the study of the changes in the ring current is an active field of research as it is a good proxy for the magnetic activity. The curlometer technique allows the current density to be calculated from the magnetic field measured at four different positions inside a given current sheet using the Maxwell-Ampere's law. In 2009, the CLUSTER perigee pass was located at about 2 RE allowing a study of the ring current deep inside the inner magnetosphere, where the pressure gradient is expected to invert direction. In this paper, we use the curlometer in such an orbit. As the method has never been used so deep inside the inner magnetosphere, this study is a test of the curlometer in a part of the magnetosphere where the magnetic field is very high (about 4000 nT) and changes over small distances (ΔB = 1nT in 1000 km). To do so, the curlometer has been applied to calculate the current density from measured and modelled magnetic fields and for different sizes of the tetrahedron. The results show that the current density cannot be calculated using the curlometer technique at low altitude perigee passes, but that the method may be accurate in a [3 RE; 5 RE] or a [6 RE; 8.3 RE] L-shell range. It also demonstrates that the parameters used to estimate the accuracy of the method are necessary, but not sufficient conditions.

scholarly journals Are the photospheric sunspots magnetically force-free in nature?

2010 ◽  
Vol 6 (S273) ◽  
pp. 333-337 ◽  
Author(s):  
Sanjiv Kumar Tiwari
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Magnetic Fields ◽  
Magnetic Energy ◽  
Sufficient Conditions ◽  
Field Measurements ◽  
Magnetic Behaviour ◽  
Optical Telescope ◽  
Energy Gradient ◽  
Necessary And Sufficient

AbstractIn a force-free magnetic field, there is no interaction of field and the plasma in the surrounding atmosphere i.e., electric currents are aligned with the magnetic field, giving rise to zero Lorentz force. The computation of many magnetic parameters like magnetic energy, gradient of twist of sunspot magnetic fields (computed from the force-free parameter α), including any kind of extrapolations heavily hinge on the force-free approximation of the photospheric magnetic fields. The force-free magnetic behaviour of the photospheric sunspot fields has been examined by Metcalf et al. (1995) and Moon et al. (2002) ending with inconsistent results. Metcalf et al. (1995) concluded that the photospheric magnetic fields are far from the force-free nature whereas Moon et al. (2002) found the that the photospheric magnetic fields are not so far from the force-free nature as conventionally regarded. The accurate photospheric vector field measurements with high resolution are needed to examine the force-free nature of sunspots. We use high resolution vector magnetograms obtained from the Solar Optical Telescope/Spectro-Polarimeter (SOT/SP) aboard Hinode to inspect the force-free behaviour of the photospheric sunspot magnetic fields. Both the necessary and sufficient conditions for force-freeness are examined by checking global as well as as local nature of sunspot magnetic fields. We find that the sunspot magnetic fields are very close to the force-free approximation, although they are not completely force-free on the photosphere.

OPTICAL PROPERTIES OF CUPRATE SUPERCONDUCTORS INFLUENCED BY A MAGNETIC FIELD

1991 ◽  
Vol 05 (10) ◽  
pp. 1539-1549 ◽  
Author(s):  
H. J. WEBER
Keyword(s):  
Magnetic Field ◽  
Circular Dichroism ◽  
External Magnetic Field ◽  
Time Reversal ◽  
Cuprate Superconductors ◽  
Magnetic Circular Dichroism ◽  
Magnetic Field Effects ◽  
Transmission Measurements ◽  
Circular Dichroïsm ◽  
The Magnetic Field

Reflection measurements on a one-domain single crystal of YBa 2 Cu 3 O 7-δ and transmission measurements on single crystals of Bi 2 Sr 2 CaCu 2 O 8 show a state of spontaneously broken symmetry below certain transition temperatures T s somewhat above the respective superconduction temperature T c . In both materials the sign of the effect can be controlled by an external magnetic field. In transmission measurements on films of YBa 2 Cu 3 O 7-δ near T s a remanent circular dichroism is observed after applying an external magnetic field. Furthermore, the films show a Curie-Weiss type increase of magnetic circular dichroism near T s . The magnetic field effects are considered as evidence for a state with broken time reversal symmetry below T s .

Zur phänomenologischen Begründung erweiterter Casimir-Onsagerscher Reziprozitätsbeziehungen

1968 ◽  
Vol 23 (10) ◽  
pp. 1446-1451 ◽  
Author(s):  
W. Muschik
Keyword(s):  
Time Reversal ◽  
State Variables ◽  
Balance Equations ◽  
Reciprocal Relations ◽  
First Time ◽  
Onsager Reciprocal Relations

Attempts are made to give phenomenological reasons for nonlinear Casimir-Onsager reciprocal relations. The fluxes can be defined as time derivations of state variables, or they can be explained by means of balance equations, because only their vectorial properties are used. At first, time reversal is replaced by an abstract parameter reversal from which involutoric transformations of forces and fluxes result. The connection between the parameter reversal of forces and fluxes allows to give reasons for relations which are equal to the Casimir-Onsager reciprocal relations apart from a sign. This sign is determined by experience. The connection between parameter and time reversal is discussed.

Growing plasma oscillations for symmetrical double-humped velocity distributions

1970 ◽  
Vol 4 (2) ◽  
pp. 297-300 ◽  
Author(s):  
S. W. H. Cowley
Keyword(s):  
Magnetic Field ◽  
Vlasov Equation ◽  
Zero Order ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Plasma Oscillations ◽  
Longitudinal Waves ◽  
Hot Plasma ◽  
Necessary And Sufficient ◽  
The Magnetic Field

The problem considered here is that of growing longitudinal waves which propagate in a hot plasma parallel to any magnetic field which may be present (i.e. the magnetic field is neglected in the Vlasov equation). The necessary and sufficient condition for stability was obtained by Penrose (1960) and growth rates for plasmas obeying a Maxwell zero-order velocity distribution were computed by Fried & Conte (1961).

Peculiar vortex structures in Fulde-Ferrell-Larkin-Ovchinnikov phase

2002 ◽  
Vol 12 (9) ◽  
pp. 385-388
Author(s):  
A. Buzdin ◽  
M. Houzet
Keyword(s):  
Magnetic Field ◽  
Upper Critical Field ◽  
Fflo State ◽  
First Order ◽  
State Observation ◽  
Field Versus ◽  
Excellent Candidate ◽  
Long Time ◽  
The Magnetic Field ◽  
2D Superconductors

A long time ago, it was predicted by Larkin and Ovchinnikov and Fulde and Ferrell that the non-uniform superconducting state (FFLO state) must appear in the magnetic field acting on the electron spins. Up to now, there have been no unambiguous experimental proofs in the favour of this state observation. We discuss the unusual properties of such a state, which can permit its identification. It is demonstrated that in 2D (or quasi 2D) superconductors the FFLO state leads to an appearance of a very special oscillatory - like dependence of the upper critical field versus the angle with the respect to the layers. The new solutions, corresponding to the higher Landau level functions are realized, and the vortex lattice structures are quite exotic. Corresponding vortex states reveal the zeros of superconducting order parameter with high winding numbers. The predicted quasi-oscillatory angular and temperature dependence of Bc2, as well as a cascade of first order transitions must permit the unambiguous identification of mysterious FFLO state. Very recently the magnetic-field-induced superconductivity has been observed in the quasi two-dimensional (2d) organic conductor (BETS)2FeCI4 which is an excellent candidate for the observation of the discussed effects.

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