scholarly journals A RIGOROUS APPROACH TO THE MAGNETIC RESPONSE IN DISORDERED SYSTEMS

2012 ◽  
Vol 24 (08) ◽  
pp. 1250022 ◽  
Author(s):  
PHILIPPE BRIET ◽  
BAPTISTE SAVOIE
Keyword(s):  
Disordered Systems ◽  
Zero Field ◽  
Quantum Gas ◽  
Random Potentials ◽  
3 Dimensional ◽  
Disordered Solids ◽  
Rigorous Approach ◽  
Diamagnetic Behavior ◽  
Thermodynamic Limits ◽  
Grand Canonical

This paper is a part of an ongoing study on the diamagnetic behavior of a 3-dimensional quantum gas of non-interacting charged particles subjected to an external uniform magnetic field together with a random electric potential. We prove the existence of an almost-sure non-random thermodynamic limit for the grand-canonical pressure, magnetization and zero-field orbital magnetic susceptibility. We also give an explicit formulation of these thermodynamic limits. Our results cover a wide class of physically relevant random potentials which model not only crystalline disordered solids, but also amorphous solids.

Quantum gas in an external field: Exact grand canonical expressions and numerical treatment

1999 ◽  
Vol 59 (1) ◽  
pp. 168-176 ◽  
Author(s):  
P. N. Vorontsov-Velyaminov ◽  
S. D. Ivanov ◽  
R. I. Gorbunov
Keyword(s):  
External Field ◽  
Quantum Gas ◽  
Numerical Treatment ◽  
Grand Canonical

A structural approach to vibrational properties ranging from crystals to disordered systems

Soft Matter ◽  
2021 ◽  
Author(s):  
Xin Tan ◽  
Ying Guo ◽  
Duan Huang ◽  
Ling Zhang
Keyword(s):  
Disordered Systems ◽  
Structural Disorder ◽  
Structural Approach ◽  
Vibrational Properties ◽  
Disordered Solids ◽  
Intense Debate

Many scientists generally attribute the vibrational anomalies of disordered solids to the structural disorder, which, however, is still under intense debate.

scholarly journals Asymptotic Growth of the Local Ground-State Entropy of the Ideal Fermi Gas in a Constant Magnetic Field

2020 ◽  
Author(s):  
Hajo Leschke ◽  
Alexander V. Sobolev ◽  
Wolfgang Spitzer
Keyword(s):  
Magnetic Field ◽  
Ground State ◽  
Constant Magnetic Field ◽  
Chemical Potential ◽  
Fermi Gas ◽  
Von Neumann Entropy ◽  
Zero Field ◽  
Quantum Gas ◽  
Asymptotic Growth ◽  
The Ideal

AbstractWe consider the ideal Fermi gas of indistinguishable particles without spin but with electric charge, confined to a Euclidean plane $${{\mathbb {R}}}^2$$ R 2 perpendicular to an external constant magnetic field of strength $$B>0$$ B > 0 . We assume this (infinite) quantum gas to be in thermal equilibrium at zero temperature, that is, in its ground state with chemical potential $$\mu \ge B$$ μ ≥ B (in suitable physical units). For this (pure) state we define its local entropy $$S(\Lambda )$$ S ( Λ ) associated with a bounded (sub)region $$\Lambda \subset {{\mathbb {R}}}^2$$ Λ ⊂ R 2 as the von Neumann entropy of the (mixed) local substate obtained by reducing the infinite-area ground state to this region $$\Lambda $$ Λ of finite area $$|\Lambda |$$ | Λ | . In this setting we prove that the leading asymptotic growth of $$S(L\Lambda )$$ S ( L Λ ) , as the dimensionless scaling parameter $$L>0$$ L > 0 tends to infinity, has the form $$L\sqrt{B}|\partial \Lambda |$$ L B | ∂ Λ | up to a precisely given (positive multiplicative) coefficient which is independent of $$\Lambda $$ Λ and dependent on B and $$\mu $$ μ only through the integer part of $$(\mu /B-1)/2$$ ( μ / B - 1 ) / 2 . Here we have assumed the boundary curve $$\partial \Lambda $$ ∂ Λ of $$\Lambda $$ Λ to be sufficiently smooth which, in particular, ensures that its arc length $$|\partial \Lambda |$$ | ∂ Λ | is well-defined. This result is in agreement with a so-called area-law scaling (for two spatial dimensions). It contrasts the zero-field case $$B=0$$ B = 0 , where an additional logarithmic factor $$\ln (L)$$ ln ( L ) is known to be present. We also have a similar result, with a slightly more explicit coefficient, for the simpler situation where the underlying single-particle Hamiltonian, known as the Landau Hamiltonian, is restricted from its natural Hilbert space $$\text{ L}^2({{\mathbb {R}}}^2)$$ L 2 ( R 2 ) to the eigenspace of a single but arbitrary Landau level. Both results extend to the whole one-parameter family of quantum Rényi entropies. As opposed to the case $$B=0$$ B = 0 , the corresponding asymptotic coefficients depend on the Rényi index in a non-trivial way.

Three-Dimensional Reconstruction Using Stereo Pairs from Serial Thick Sections

1977 ◽  
Vol 35 ◽  
pp. 562-563
Author(s):  
Robert Glaeser ◽  
Thomas Bauer ◽  
David Grano
Keyword(s):  
Three Dimensional ◽  
Dimensional Structure ◽  
Serial Sections ◽  
Thin Sections ◽  
3 Dimensional ◽  
Transmission Electron ◽  
Freeze Dried ◽  
Dimensional Reconstruction ◽  
Stereo Imagery ◽  
Whole Mounts

In transmission electron microscopy, the 3-dimensional structure of an object is usually obtained in one of two ways. For objects which can be included in one specimen, as for example with elements included in freeze- dried whole mounts and examined with a high voltage microscope, stereo pairs can be obtained which exhibit the 3-D structure of the element. For objects which can not be included in one specimen, the 3-D shape is obtained by reconstruction from serial sections. However, without stereo imagery, only detail which remains constant within the thickness of the section can be used in the reconstruction; consequently, the choice is between a low resolution reconstruction using a few thick sections and a better resolution reconstruction using many thin sections, generally a tedious chore. This paper describes an approach to 3-D reconstruction which uses stereo images of serial thick sections to reconstruct an object including detail which changes within the depth of an individual thick section.

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