36 research outputs found
Ideal quantum gases in two dimensions
Thermodynamic properties of non-relativistic bosons and fermions in two
spatial dimensions and without interactions are derived. All the virial
coefficients are the same except for the second, for which the signs are
opposite. This results in the same specific heat for the two gases. Existing
equations of state for the free anyon gas are also discussed and shown to break
down at low temperatures or high densities.Comment: 17 page
Few-electron eigenstates of concentric double quantum rings
Few-electron eigenstates confined in coupled concentric double quantum rings
are studied by the exact diagonalization technique. We show that the magnetic
field suppresses the tunnel coupling between the rings localizing the
single-electron states in the internal ring, and the few-electron states in the
external ring. The magnetic fields inducing the ground-state angular momentum
transitions are determined by the distribution of the electron charge between
the rings. The charge redistribution is translated into modifications of the
fractional Aharonov-Bohm period. We demonstrate that the electron distribution
can be deduced from the cusp pattern of the chemical potentials governing the
single-electron charging properties of the system. The evolution of the
electron-electron correlations to the high field limit of a classical Wigner
molecule is discussed.Comment: to appear in Physical Review
Quantum Hall Physics - hierarchies and CFT techniques
The fractional quantum Hall effect, being one of the most studied phenomena
in condensed matter physics during the past thirty years, has generated many
groundbreaking new ideas and concepts. Very early on it was realized that the
zoo of emerging states of matter would need to be understood in a systematic
manner. The first attempts to do this, by Haldane and Halperin, set an agenda
for further work which has continued to this day. Since that time the idea of
hierarchies of quasiparticles condensing to form new states has been a pillar
of our understanding of fractional quantum Hall physics. In the thirty years
that have passed since then, a number of new directions of thought have
advanced our understanding of fractional quantum Hall states, and have extended
it in new and unexpected ways. Among these directions is the extensive use of
topological quantum field theories and conformal field theories, the
application of the ideas of composite bosons and fermions, and the study of
nonabelian quantum Hall liquids. This article aims to present a comprehensive
overview of this field, including the most recent developments.Comment: added section on experimental status, 59 pages+references, 3 figure
Electron spin and charge switching in a coupled quantum dot quantum ring system
Few-electron systems confined in a quantum dot laterally coupled to a
surrounding quantum ring in the presence of an external magnetic field are
studied by exact diagonalization. The distribution of electrons between the dot
and the ring is influenced by the relative strength of the dot and ring
confinement, the gate voltage and the magnetic field which induces transitions
of electrons between the two parts of the system. These transitions are
accompanied by changes in the periodicity of the Aharonov-Bohm oscillations of
the ground-state angular momentum. The singlet-triplet splitting for a two
electron system with one electron confined in the dot and the other in the ring
exhibits piecewise linear dependence on the external field due to the
Aharonov-Bohm effect for the ring-confined electron, in contrast to smooth
oscillatory dependence of the exchange energy for laterally coupled dots in the
side-by-side geometry.Comment: to appear in PRB in August 200
Quantum rings as electron spin beam splitters
Quantum interference and spin-orbit interaction in a one-dimensional
mesoscopic semiconductor ring with one input and two output leads can act as a
spin beam splitter. Different polarization can be achieved in the two output
channels from an originally totally unpolarized incoming spin state, very much
like in a Stern-Gerlach apparatus. We determine the relevant parameters such
that the device has unit efficiency.Comment: 4 pages, 3 figures; minor change
Spintronic single qubit gate based on a quantum ring with spin-orbit interaction
In a quantum ring connected with two external leads the spin properties of an
incoming electron are modified by the spin-orbit interaction resulting in a
transformation of the qubit state carried by the spin. The ring acts as a one
qubit spintronic quantum gate whose properties can be varied by tuning the
Rashba parameter of the spin-orbit interaction, by changing the relative
position of the junctions, as well as by the size of the ring. We show that a
large class of unitary transformations can be attained with already one ring --
or a few rings in series -- including the important cases of the Z, X, and
Hadamard gates. By choosing appropriate parameters the spin transformations can
be made unitary, which corresponds to lossless gates.Comment: 4 pages, 4 figure
Number Fluctuation in an interacting trapped gas in one and two dimensions
It is well-known that the number fluctuation in the grand canonical ensemble,
which is directly proportional to the compressibility, diverges for an ideal
bose gas as T -> 0. We show that this divergence is removed when the atoms
interact in one dimension through an inverse square two-body interaction. In
two dimensions, similar results are obtained using a self-consistent
Thomas-Fermi (TF) model for a repulsive zero-range interaction. Both models may
be mapped on to a system of non-interacting particles obeying the Haldane-Wu
exclusion statistics. We also calculate the number fluctuation from the ground
state of the gas in these interacting models, and compare the grand canonical
results with those obtained from the canonical ensemble.Comment: 11 pages, 1 appendix, 3 figures. Submitted to J. Phys. B: Atomic,
Molecular & Optica
Analytical treatment of interacting Fermi gas in arbitrary dimensional harmonic trap
We study normal state properties of an interacting Fermi gas in an isotropic
harmonic trap of arbitrary dimensions. We exactly calculate the first-order
perturbation terms in the ground state energy and chemical potential, and
obtain simple analytic expressions of the total energy and chemical potential.
At zero temperature, we find that Thomas-Fermi approximation agrees well with
exact results for any dimension even though system is dilute and small, i.e.
when the Thomas-Fermi approximation is generally expected to fail. In the high
temperature (classical) region, we find interaction energy decreases in
proportion to T^(-d/2), where T is temperature and d is dimension of the
system. Effect of interaction in the ground state in two and three-dimensional
systems is also discussed.Comment: 15 pages, 4 figure
Exclusion Statistics in a trapped two-dimensional Bose gas
We study the statistical mechanics of a two-dimensional gas with a repulsive
delta function interaction, using a mean field approximation. By a direct
counting of states we establish that this model obeys exclusion statistics and
is equivalent to an ideal exclusion statistics gas.Comment: 3 pages; minor changes in notation; typos correcte
Condensation in ideal Fermi gases
I investigate the possibility of condensation in ideal Fermi systems of
general single particle density of states. For this I calculate the probability
of having exactly particles in the condensate and analyze its
maxima. The existence of such maxima at macroscopic values of indicates a
condensate. An interesting situation occurs for example in 1D systems, where
may have two maxima. One is at and another one may exist at
finite (for temperatures bellow a certain condensation temperature). This
suggests the existence of a first order phase transition. % The calculation of
allows for the exploration of ensemble equivalence of Fermi systems
from a new perspective.Comment: 8 pages with 1 figure. Will appear in J. Phys. A: Math. Gen. Changes
(minor): I updated Ref. [9] and its citation in the text. I introduced
citation for figure 1 in the tex