arXiv subjects

M. E. S. Borelli

Publications and source records attributed to M. E. S. Borelli.

6 recordsLinked to original sources

arXiv2000

Self-Consistent Effective Action for Quantum Particle with Space-Dependent Mass

We calculate the quantum corrections to the classical action of a particle with coordinate-dependent mass. The result is made self-consistent by a variational approach, thus making it applicable to strong-couplings and singular potentials. By including thermal fluctuations, the we obtain an effective action whose classical Euler-Lagrange equation describes the motion of a particle including quantum and thermal effects.

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

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↗

arXiv1999

Derivative Expansion of One-Loop Effective Energy of Stiff Membranes with Tension

With help of a derivative expansion, the one-loop corrections to the energy functional of a nearly flat, stiff membrane with tension due to thermal fluctuations are calculated in the Monge parametrization. Contrary to previous studies, an arbitrary tilt of the surface is allowed to exhibit the nontrivial relations between the different, highly nonlinear terms accompanying the ultraviolet divergences. These terms are shown to have precisely the same form as those in the original energy functional, as necessary for renormalizability. Also infrared divergences arise. These, however, are shown to cancel in a nontrivial way.

cond-mat↗