632 research outputs found
Moebius Structure of the Spectral Space of Schroedinger Operators with Point Interaction
The Schroedinger operator with point interaction in one dimension has a U(2)
family of self-adjoint extensions. We study the spectrum of the operator and
show that (i) the spectrum is uniquely determined by the eigenvalues of the
matrix U belonging to U(2) that characterizes the extension, and that (ii) the
space of distinct spectra is given by the orbifold T^2/Z_2 which is a Moebius
strip with boundary. We employ a parametrization of U(2) that admits a direct
physical interpretation and furnishes a coherent framework to realize the
spectral duality and anholonomy recently found. This allows us to find that
(iii) physically distinct point interactions form a three-parameter quotient
space of the U(2) family.Comment: 16 pages, 2 figure
s-wave scattering and the zero-range limit of the finite square well in arbitrary dimensions
We examine the zero-range limit of the finite square well in arbitrary
dimensions through a systematic analysis of the reduced, s-wave two-body
time-independent Schr\"odinger equation. A natural consequence of our
investigation is the requirement of a delta-function multiplied by a
regularization operator to model the zero-range limit of the finite-square well
when the dimensionality is greater than one. The case of two dimensions turns
out to be surprisingly subtle, and needs to be treated separately from all
other dimensions
Thermodynamic hierarchies of evolution equations
Non-equilibrium thermodynamics with internal variables introduces a natural
hierarchical arrangement of evolution equations. Three examples are shown: a
hierarchy of linear constitutive equations in thermodynamic rhelogy with a
single internal variable, a hierarchy of wave equations in the theory of
generalized continua with dual internal variables and a hierarchical
arrangement of the Fourier equation in the theory of heat conduction with
current multipliers.Comment: 7 pages, 1 figur
Deviation from the Fourier law in room-temperature heat pulse experiments
We report heat pulse experiments at room temperature that cannot be described
by Fourier's law. The experimental data is modelled properly by the
Guyer--Krumhansl equation, in its over-diffusion regime. The phenomenon is due
to conduction channels with differing conductivities, and parallel to the
direction of the heat flux.Comment: 9 pages, 4 figure
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