70 research outputs found
Localization, Dirac Fermions and Onsager Universality
Disordered systems exhibiting exponential localization are mapped to
anisotropic spin chains with localization length being related to the
anisotropy of the spin model. This relates localization phenomenon in fermions
to the rotational symmetry breaking in the critical spin chains. One of the
intriguing consequence is that the statement of Onsager universality in spin
chains implies universality of the localized fermions where the fluctuations in
localized wave functions are universal. We further show that the fluctuations
about localized nonrelativistic fermions describe relativistic fermions. This
provides a new approach to understand the absence of localization in disordered
Dirac fermions. We investigate how disorder affects well known universality of
the spin chains by examining the multifractal exponents. Finally, we examine
the effects of correlations on the localization characteristics of relativistic
fermions.Comment: To appear in EPJ; Proceedings of Internation conference on Geometry
and Integrabilit
Geometric Phase and Classical-Quantum Correspondence
We study the geometric phase factors underlying the classical and the
corresponding quantum dynamics of a driven nonlinear oscillator exhibiting
chaotic dynamics. For the classical problem, we compute the geometric phase
factors associated with the phase space trajectories using Frenet-Serret
formulation. For the corresponding quantum problem, the geometric phase
associated with the time evolution of the wave function is computed. Our
studies suggest that the classical geometric phase may be related to the the
difference in the quantum geometric phases between two neighboring eigenstates.Comment: Copy with higher resolution figures can be obtained from
http://physics.gmu.edu/~isatija by clicking on publications. to appear in the
Yukawa Institute conference proceedings, {\it Quantum Mechanics and Chaos:
From Fundamental Problems through Nano-Science} (2003
Solitons in a hard-core bosonic system: Gross-Pitaevskii type and beyond
A unified formulation that obtains solitary waves for various background
densities in the Bose-Einstein condensate of a system of hard-core bosons with
nearest neighbor attractive interactions is presented.
In general, two species of solitons appear: A nonpersistent (NP) type that
fully delocalizes at its maximum speed, and a persistent (P) type that survives
even at its maximum speed, and transforms into a periodic train of solitons
above this speed. When the background condensate density is nonzero, both
species coexist, the soliton is associated with a constant intrinsic frequency,
and its maximum speed is the speed of sound. In contrast, when the background
condensate density is zero, the system has neither a fixed frequency, nor a
speed of sound. Here, the maximum soliton speed depends on the frequency, which
can be tuned to lead to a cross-over between the NP-type and the P-type at a
certain critical frequency, determined by the energy parameters of the system.
We provide a single functional form for the soliton profile, from which diverse
characteristics for various background densities can be obtained. Using the
mapping to spin systems enables us to characterize the corresponding class of
magnetic solitons in
Heisenberg spin chains with different types of anisotropy, in a unified
fashion
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