1,376 research outputs found
Comment on Path Integral Derivation of Schr\"odinger Equation in Spaces with Curvature and Torsion
We present a derivation of the Schr\"odinger equation for a path integral of
a point particle in a space with curvature and torsion which is considerably
shorter and more elegant than what is commonly found in the literature.Comment: LaTeX file in sr
Phase diagram for interacting Bose gases
We propose a new form of the inversion method in terms of a selfenergy
expansion to access the phase diagram of the Bose-Einstein transition. The
dependence of the critical temperature on the interaction parameter is
calculated. This is discussed with the help of a new condition for
Bose-Einstein condensation in interacting systems which follows from the pole
of the T-matrix in the same way as from the divergence of the medium-dependent
scattering length. A many-body approximation consisting of screened ladder
diagrams is proposed which describes the Monte Carlo data more appropriately.
The specific results are that a non-selfconsistent T-matrix leads to a linear
coefficient in leading order of 4.7, the screened ladder approximation to 2.3,
and the selfconsistent T-matrix due to the effective mass to a coefficient of
1.3 close to the Monte Carlo data
Brownian motion of Massive Particle in a Space with Curvature and Torsion and Crystals with Defects
We develop a theory of Brownian motion of a massive particle, including the
effects of inertia (Kramers' problem), in spaces with curvature and torsion.
This is done by invoking the recently discovered generalized equivalence
principle, according to which the equations of motion of a point particle in
such spaces can be obtained from the Newton equation in euclidean space by
means of a nonholonomic mapping. By this principle, the known Langevin equation
in euclidean space goes over into the correct Langevin equation in the Cartan
space. This, in turn, serves to derive the Kubo and Fokker-Planck equations
satisfied by the particle distribution as a function of time in such a space.
The theory can be applied to classical diffusion processes in crystals with
defects.Comment: LaTeX, http://www.physik.fu-berlin.de/kleinert.htm
Five-Loop Vacuum Energy Beta Function in phi^4 Theory with O(N)-Symmetric and Cubic Interactions
The beta function of the vacuum energy density is analytically computed at
the five-loop level in O(N)-symmetric phi^4 theory, using dimensional
regularization in conjunction with the MSbar scheme. The result for the case of
a cubic anisotropy is also given. It is pointed out how to also obtain the beta
function of the coupling and the gamma function of the mass from vacuum graphs.
This method may be easier than traditional approaches.Comment: 16 pages, LaTeX; "note added" fixe
Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops
The shift of the Bose-Einstein condensation temperature for a homogenous
weakly interacting Bose gas in leading order in the scattering length `a' is
computed for given particle density `n.' Variational perturbation theory is
used to resum the corresponding perturbative series for Delta/Nu in a
classical three-dimensional scalar field theory with coupling `u' and where the
physical case of N=2 field components is generalized to arbitrary N. Our
results for N=1,2,4 are in agreement with recent Monte-Carlo simulations; for
N=2, we obtain Delta T_c/T_c = 1.27 +/- 0.11 a n^(1/3). We use seven-loop
perturbative coefficients, extending earlier work by one loop order.Comment: 8 pages; typos and errors of presentation fixed; beautifications;
results unchange
Criterion for Dominance of Directional over Size Fluctuations in Destroying Order
For systems exhibiting a second-order phase transition with a spontaneously
broken continuous O(N)-symmetry at low temperature, we give a criterion for
judging at which temperature T_K long-range directional fluctuations of the
order field destroy the order when approaching the critical temperature from
below. The temperature T_K lies always significantly below the famous Ginzburg
temperature T_G at which size fluctuations of finite range in the order field
become important.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/re3.html#29
Reentrant Phenomenon in Quantum Phase Diagram of Optical Boson Lattice
We calculate the location of the quantum phase transitions of a bose gas
trapped in an optical lattice as a function of effective scattering length
a_{\eff} and temperature . Knowledge of recent high-loop results on the
shift of the critical temperature at weak couplings is used to locate a {\em
nose} in the phase diagram above the free Bose-Einstein critical temperature
, thus predicting the existence of a reentrant transition {\em
above} , where a condensate should form when {\em increasing}
a_{\eff}. At zero temperature, the transition to the normal phase produces
the experimentally observed Mott insulator.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.htm
Perturbation Theory for Path Integrals of Stiff Polymers
The wormlike chain model of stiff polymers is a nonlinear -model in
one spacetime dimension in which the ends are fluctuating freely. This causes
important differences with respect to the presently available theory which
exists only for periodic and Dirichlet boundary conditions. We modify this
theory appropriately and show how to perform a systematic large-stiffness
expansions for all physically interesting quantities in powers of ,
where is the length and the persistence length of the polymer. This
requires special procedures for regularizing highly divergent Feynman integrals
which we have developed in previous work. We show that by adding to the
unperturbed action a correction term , we can calculate
all Feynman diagrams with Green functions satisfying Neumann boundary
conditions. Our expansions yield, order by order, properly normalized
end-to-end distribution function in arbitrary dimensions , its even and odd
moments, and the two-point correlation function
Magnetic permeability of near-critical 3d abelian Higgs model and duality
The three-dimensional abelian Higgs model has been argued to be dual to a
scalar field theory with a global U(1) symmetry. We show that this duality,
together with the scaling and universality hypotheses, implies a scaling law
for the magnetic permeablity chi_m near the line of second order phase
transition: chi_m ~ t^nu, where t is the deviation from the critical line and
nu ~ 0.67 is a critical exponent of the O(2) universality class. We also show
that exactly on the critical lines, the dependence of magnetic induction on
external magnetic field is quadratic, with a proportionality coefficient
depending only on the gauge coupling. These predictions provide a way for
testing the duality conjecture on the lattice in the Coulomb phase and at the
phase transion.Comment: 11 pages; updated references and small changes, published versio
Strings with Negative Stiffness and Hyperfine Structure
We propose a new string model by adding a higher-order gradient term to the
rigid string, so that the stiffness can be positive or negative without loosing
stability. In the large-D approximation, the model has three phases, one of
which with a new type of generalized "antiferromagnetic" orientational
correlations. We find an infrared-stable fixed point describing world-sheets
with vanishing tension and Hausdorff dimension D_H=2. Crumpling is prevented by
the new term which suppresses configurations with rapidly changing extrinsic
curvature.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re27
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