2,907 research outputs found
Exact Momentum Distribution of a Fermi Gas in One Dimension
We introduce an exactly solvable model of a fermi gas in one dimension and
compute the momentum distribution exactly. This is based on a generalisation of
the ideas of bosonization in one dimension. It is shown that in the RPA
limit(the ultra-high density limit) the answers we get are the exact answers
for a homogeneous fermi gas interacting via a two-body repulsive coulomb
interaction. Furthermore, the solution may be obtained exactly for arbitrary
functional forms of the interaction, so long as it is purely repulsive. No
linearization of the bare fermion dispersion is required. We find that for the
interaction considered, the fermi surface is intact for weak repulsion and is
destroyed only for sufficiently strong repulsion. Comparison with other models
like the supersymmetric t-J model with inverse square interactions is made.Comment: RevTex, 5 pages, no figures., modified following ref. comments, more
detailed explanations, resutls same, one new ref. adde
Exact Dynamical Structure Factor of a Bose Liquid
Based on ideas introduced in a previous preprint cond-mat/9701206 we propose
an exactly solvable model of bosons interacting amongst themselves via a
Van-der Waal-like repulsive interaction, and compute both the filling fraction
and the dynamical structure factor exactly. The novelty of this approach
involves introducing, analogous to Fermi sea (or surface) displacements, Bose
fields that in this case, correspond to fluctuations of the Bose condensate.
The exact dynamical structure factor has a coherent part that corresponds to
the Bogoliubov spectrum and an incoherent part that is a result of
correlations.Comment: RevTex, 6 pages, no figures, replaced previously empty fil
A.C. Conductivity of a Disordered Metal
The degenerate free Fermi gas coupled to a random potential is used to
compute a.c. conductivity in various dimensions. We first formally diagonalise
the hamiltonian using an appropriate basis that is a functional of the disorder
potential. Then we compute the a.c. conductivity at zero temperature using the
Kubo formula. This a.c. conductivity is a functional of the disordered
potential. The wavefunction of extended states is written as exponential of the
logarithm. We use the cumulant expansion to compute the disordered averaged
a.c. conductivity for Gaussian disorder. The formula is valid if a certain
linearization approximation is valid in the long-wavelength limit.Comment: 22 pages, no figs., Plain LaTe
Myopic Bosonization
As the title suggests, this is an attempt at bosonizing fermions in any
number of dimensions without paying attention to the fact that the Fermi
surface is an extended object. One is tempted to introduce the density
fluctuation and its conjugate and recast the interacting problem in terms of
these canonical Bose fields. However, we find that the attempt is short-sighted
figuratively as well for the same reason.
But surprisingly, this flaw, which manifests itself as an inconsistency
between Menikoff-Sharp's construction of the kinetic energy operator in terms
of currents and densities, and our ansatz for this operator, is nevertheless
able to reproduce(although reluctantly) many salient features of the free
theory.
Buoyed by this success, we solve the interacting problem and compute the full
propagator.Comment: 3 pages RevTe
Microscopic Origin of Spatial Coherence and Wolf Shifts
We show that the vacuum of electromagnetic field has intrinsic partial
spatial coherence in frequency domain which effectively extends over regions of
the order of wavelength . This spatial coherence leads to a dynamical
coupling between atoms and is the cause of source correlations and Wolf shifts.
We show how the source spatial correlations can lead to tailor made coherent
emissions. We discuss the universality of source correlation effects and
presents several application.Comment: 7 pages, 8 figure
Xray-Edge Spectra From Sea-Bosons-I
The well-studied phenomenon of X-ray edge singularities is revisited using
the sea-boson approach that has recently been placed on a rigorous footing. We
are able to reproduce the well-known result namely, Mahan's power law
divergences. Unlike the work of Schotte and Schotte, no linearization of the
bare fermion dispersion is needed, which, by their own admission, is a source
of some difficulty. Our approach also brings out some differences between the
different dimensions which is not present in their work. Finally, our work also
allows for easy generalization to potentials more realistic than the simple
delta-function used commonly in the literature.Comment: 8 pages, regular LaTeX, one inbuilt fi
Bosonization and Quantum Hydrodynamics
It is shown that it is possible to bosonize fermions in any number of
dimensions using the hydrodynamic variables, namely the velocity potential and
density. The slow part of the Fermi field is defined irrespective of
dimensionality and the commutators of this field with currents and densities
are exponentiated using the velocity potential as conjugate to the density. An
action in terms of these canonical bosonic variables is proposed that
reproduces the correct current and density correlations. This formalism in one
dimension is shown to be equivalent to the Tomonaga-Luttinger approach as it
leads to the same propagator and exponents. We compute the one-particle
properties of a spinless homogeneous Fermi system in two spatial dimensions
with long-range gauge interactions and highlight the metal-insulator transition
in the system. A general formula for the generating function of density
correlations is derived that is valid beyond the random phase approximation.
Finally, we write down a formula for the annihilation operator in momentum
space directly in terms of number conserving products of Fermi fields.Comment: Published version plus never before seen action footage of a new
proo
Quenched Disorder From Sea-Bosons
The degenerate Fermi gas coupled to a random potential is used to study
metal-insulator transitions in various dimensions.
We first recast the problem in the sea-boson language that allows for an easy
evaluation of important physical attributes.
We evaluate the dynamical number-number correlation function and from this
compute the a.c. conductivity.
We find that the d.c. conductivity vanishes in one and two dimensions.
For a hamiltonian that forbids scattering of an electron from within the
Fermi surface to another state within the Fermi surface we find that there is
no metal-insulator transition in three dimensions either.Comment: 8 pages, Plain LaTe
Hydrodynamic Formulation of the Hubbard Model
In this article, we show how to recast the Hubbard model in one dimension in
a hydrodynamic language and use the path integral approach to compute the
one-particle Green function.
We compare with the Bethe ansatz results of
Schulz and find exact agreement with the formulas for spin and charge
velocities and anomalous exponent in weak coupling regime.
These methods may be naturally generalized to more than one dimension by
simply promoting wavenumbers to wavevectors.Comment: 7 pages, no fig
Momentum Distribution of a Weakly Coupled Fermi Gas
We apply the sea-boson method to compute the momentum distribution of a
spinless continuum Fermi gas in two space dimensions with short-range repulsive
interactions. We find that the ground state of the system is a Landau Fermi
liquid(). We also apply this method to study the
one-dimensional system when the interactions are long-ranged gauge
interactions. We map the Wigner crystal phase of this system.Comment: 5 pages, plain LaTe
- …