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H. Kleinert

Publications and source records attributed to H. Kleinert.

At least 73 records · Page 4Linked to original sources
arXiv2000

Variational Approach to Hydrogen Atom in Uniform Magnetic Field of Arbitrary Strength

Extending the Feynman-Kleinert variational approach, we calculate the temperature-dependent effective classical potential governing the quantum statistics of a hydrogen atom in a uniform magnetic at all temperatures. The zero-temperature limit yields the binding energy of the electron which is quite accurate for all magnetic field strengths and exhibits, in particular, the correct logarithmic growth at large fields.

quant-ph↗
arXiv2000

Phases of a Stack of Membranes at Large-d

The phase diagram of a stack of tensionless membranes with nonlinear curvature energy and vertical harmonic interaction is calculated exactly in a large number of dimensions of configuration space. At low temperatures, the system forms a lamellar phase with spontaneously broken translational symmetry in the vertical direction. At a critical temperature, the stack disorders vertically in a melting-like transition. The critical temperature is determined as a function of the interlayer separation l.

cond-mat↗
arXiv2000

Vertical Melting of a Stack of Membranes

A stack of tensionless membranes with nonlinear curvature energy and vertical harmonic interaction is studied. At low temperatures, the system forms a lamellar phase. At a critical temperature, the stack disorders vertically in a melting-like transition.

cond-mat↗
arXiv2000

Calculation of Second Topological Moment of Two Entangled Polymers

We set up a Chern-Simons theory for the entanglement of two polymers P_1 and P_2, and calculate the second topological moment , where m is the linking number. The result applies approximately to a polymer in an ensemble of many others, if these are considered as a single very long effective polymer.

cond-mat↗
arXiv2000

Quantum Statistical Mechanics of Nonrelativistic Membranes: Crumpling Transition at Finite Temperature

The effect of quantum fluctuations on a nearly flat, nonrelativistic two-dimensional membrane with extrinsic curvature stiffness and tension is investigated. The renormalization group analysis is carried out in first-order perturbative theory. In contrast to thermal fluctuations, which soften the membrane at large scales and turn it into a crumpled surface, quantum fluctuations are found to {\em stiffen} the membrane, so that it exhibits a Hausdorff dimension equal to two. The large-scale behavior of the membrane is further studied at finite temperature, where a nontrivial fixed point is found, signaling a crumpling transition.

cond-mat↗
arXiv2000

Decrumpling membranes by quantum effects

The phase diagram of an incompressible fluid membrane subject to quantum and thermal fluctuations is calculated exactly in a large number of dimensions of configuration space. At zero temperature, a crumpling transition is found at a critical bending rigidity $1/α_{\rm c}$. For membranes of fixed lateral size, a crumpling transition occurs at nonzero temperatures in an auxiliary mean field approximation. As the lateral size L of the membrane becomes large, the flat regime shrinks with $1/\ln L$.

cond-mat↗
arXiv2000

Coordinate Independence of of Quantum-Mechanical Path Integrals

We develop simple rules for performing integrals over products of distributions in coordinate space. Such products occur in perturbation expansions of path integrals in curvilinear coordinates, where the interactions contain terms of the form dot q^2 q^n, which give rise to highly singular Feynman integrals. The new rules ensure the invariance of perturbatively defined path integrals under coordinate transformations.

quant-ph↗
arXiv2000

No Spontaneous Breakdown of Chiral Symmetry in Nambu-Jona-Lasinio Model

We argue that the spontaneous breakdown of symmetry in the chirally symmetric Nambu--Jona-Lasinio model which was supposed to illustrate the origin of the low mass of pions in hadron physics does not occur due to strong fluctuations in the sigma - pi field space. Although quarks acquire a constituent mass, sigma and pi turn out to have equal heavy masses of the order of the constituent quark mass.

hep-ph↗
arXiv2000

Reparametrization Invariance of Perturbatively Defined Path Integrals. II. Integrating Products of Distributions

We show how to perform integrals over products of distributions in coordinate space such as to reproduce the results of momentum space Feynman integrals in dimensional regularization. This ensures the invariance of path integrals under coordinate transformations. The integrals are uniquely defined by expressing the propagators in 1- epsilon dimensions in terms of modified Bessel functions.

quant-ph↗
arXiv1999

Recursive Graphical Construction for Feynman Diagrams of Quantum Electrodynamics

We present a method for a recursive graphical construction of Feynman diagrams with their correct multiplicities in quantum electrodynamics. The method is first applied to find all diagrams contributing to the vacuum energy from which all n-point functions are derived by functional differentiation with respect to electron and photon propagators, and to the interaction. Basis for our construction is a functional differential equation obeyed by the vacuum energy when considered as a functional of the free propagators and the interaction. Our method does not employ external sources in contrast to traditional approaches.

hep-th↗
arXiv1999

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.

cond-mat↗
arXiv1999

No Massless Pions in Nambu-Jona-Lasinio Model due to Chiral Fluctuations

In contrast to common belief, the chirally symmetric Nambu--Jona-Lasinio model does not contain massless pions, due to strong chiral fluctuations. Although quarks acquire spontaneously a nonzero constituent mass $M$, pions have a nonzero mass equal to the mass of $ \s $-mesons, both being of the order of $M$. This result is found in several cutoff schemes. Our derivation is nonperturbative, but involves a simple approximation (London limit) which should, however, receive only quantitative, no qualitative corrections.

hep-ph↗
arXiv1999

Autoparallels From a New Action Principle

We present a simpler and more powerful version of the recently-discovered action principle for the motion of a spinless point particle in spacetimes with curvature and torsion. The surprising feature of the new principle is that an action involving only the metric can produce an equation of motion with a torsion force, thus changing geodesics to autoparallels. This additional torsion force arises from a noncommutativity of variations with parameter derivatives of the paths due to the closure failure of parallelograms in the presence of torsion

gr-qc↗
arXiv1999

Nonperturbative XY-model approach to strong coupling superconductivity in two and three dimensions

For an electron gas with delta-function attraction we investigate the crossover from weak- to strong-coupling supercoductivity in two and three dimensions. We derive analytic expressions for the stiffness of phase fluctuations and set up effective XY-models which serve to determine nonperturbatively the temperature of phase decoherence where superconductivity breaks down. We find the transition temperature T_c as a monotonous function of the coupling strength and carrier density both in two and three dimensions, and give analytic formulas for the merging of the temperature of phase decoherence with the temperature of pair formation in the weak-coupling limit.

cond-mat↗
arXiv1999

Reparametrization Invariance of Path Integrals

We demonstrate the reparametrization invariance of perturbatively defined one-dimensional functional integrals up to the three-loop level for a path integral of a quantum-mechanical point particle in a box. We exhibit the origin of the failure of earlier authors to establish reparametrization invariance which led them to introduce, superfluously, a compensating potential depending on the connection of the coordinate system. We show that problems with invariance are absent by defining path integrals as the epsilon-> 0 -limit of 1+ epsilon -dimensional functional integrals.

hep-th↗