Anatomy of the trace formula for the baker's map

The structure of the trace formula for quantum maps on a compact phase space is analyzed. An explicit expression for the functional determinant in terms of a finite number of traces is derived which is algebraic and independent of any approximation. For the specific case of the baker's map, its simple structure allows the implementation of a symbolic decomposition of the propagator which is exact and which has the structure of usual semiclassical formulas. The method allows the testing of the accuracy of the individual contribution of each periodic orbit to the functional determinant.     

A superanalog of the Selberg trace formula and multiloop contributions for fermionic strings

An analog of the classical Selberg trace formula is given for discrete groups, acting on the upper complex half-superplane. Applications to the fermionic string measure on the moduli superspace are discussed.     

Geometric quantization of Hamiltonian flows and the Gutzwiller trace formula

Letters in Mathematical Physics - We use the theory of Berezin–Toeplitz operators of Ma and Marinescu to study the quantum Hamiltonian dynamics associated with classical Hamiltonian flows...     

Application of the diffraction trace formula to the three-disk scattering system

The diffraction trace formula derived previously and the spectral determinant are tested on the open three-disk scattering system. The system contains a generic and exponentially growing number of diffraction periodic orbits. In spite of this it is shown that even the scattering resonances with large imaginary part can be reproduced semiclassically. The nontrivial interplay of the diffraction periodic orbits with the usual geometrical orbits produces the fine structure of the complicated spectrum of scattering resonances, which are beyond the resolution of the conventional periodic orbit theory.     

Kernel and trace formula for the exponential of the Laplace-Beltrami operator on a decorated graph

For the kernel of the Laplace operator Δ^Λ with potential Σ _j=1 ^k c _j δ _{q j} (x) on a manifold, (the operator is given by a Lagrangian plane Λ ⊂ ℂ ^k ⊕ ℂ ^k ), an isomorphism Γ: ker Δ^Λ → Λ ∩ L is described, where L is a special Lagrangian plane (whose explicit form is evaluated). A similar assertion holds for the Laplace operator on a decorated graph; for such a graph (obtained by decorating a connected finite graph with n edges and v vertices) with “continuity” conditions, the inequality 1 ≤ dimker ≤ n − v + 2 is obtained. It is also proved that the quantity n − v + 1-dim ker cannot reduce when adding new edges and manifolds. The first terms of the expansion of Tr(exp(-tH ^Λ)) are found. Dedicated to the memory of V. A. Geyler     

Experimental test of a trace formula for a chaotic three-dimensional microwave cavity

We have measured resonance spectra in a superconducting microwave cavity with the shape of a three-dimensional generalized Bunimovich stadium billiard and analyzed their spectral fluctuation properties. The experimental length spectrum exhibits contributions from periodic orbits of nongeneric modes and from unstable periodic orbits of the underlying classical system. It is well reproduced by our theoretical calculations based on the trace formula derived by Balian and Duplantier for chaotic electromagnetic cavities.     

A new formula for the saddle-to-scission time

We propose a new formula for the saddle-to-scission time that is more general that the one based on Kramers' approach. Its validity and applicability is then studied in detail. Such a formula is useful for the evaluation of the fission time of very heavy nuclei.     

A spin-asymmetry term for the mass formula

From the shell model the number of nucleons with total angular momentum $\text{j = l+}\text{1}\text{2}$ in an average nucleus exceeds that of nucleons with $\text{j = l?}\text{1}\text{2}$. The spin-orbit and the spin-asymmetry energy brought about by this polarisation are shown to contribute on the average ?1.5 MeV to the surface energy coefficient. The fluctuating difference between the polarisation energy and its smooth approximation is argued to be an important component of the microscopic shell term in actual mass formulae.     

A new nodal expansion for classical plasmas

In calculating the equation of state for plasmas we find that diagrammatic expansions for the free energy become unwieldy at high density. At best, many terms must be retained in order to obtain meaningful results. We present a new expansion technique which can be applied to plasmas in the interiors of Jupiter and white dwarf stars. In such cases the older techniques are unsatisfactory because of the size of the ion coupling parameter. Our work yields expansions for which this parameter is supplanted by ion correlation functions, which can be supplied by external computations. In this paper we assume a two-species plasma of classical particles, thereby focusing on combinatorial techniques. The final result is a new nodal expansion in terms of ion correlation functions and an electron coupling parameter.     

A formula for charmonium suppression

In this work a formula for charmonium suppression obtained by Matsui in 1989 is analytically generalized for the case of complex $c\bar c$ potential described by a 3-dimensional and isotropic time-dependent harmonic oscillator (THO). It is suggested that under certain scheme the formula can be applied to describe J/?? suppression in heavy-ion collisions at CERN-SPS, RHIC, and LHC with the advantage of analytical tractability.     

A difference-equation formalism for the nodal domains of separable billiards

Recently, the nodal domain counts of planar, integrable billiards with Dirichlet boundary conditions were shown to satisfy certain difference equations in Samajdar and Jain (2014). The exact solutions of these equations give the number of domains explicitly. For complete generality, we demonstrate this novel formulation for three additional separable systems and thus extend the statement to all integrable billiards.     

A microscopic formula for actinide masses

A fully microscopic actinide mass formula is derived using the fermion dynamical symmetry model approximation to the spherical shell model. A rich dynamical symmetry phase structure is confirmed, and the mass formula fits the masses of 322 nuclei with an RMS deviation of 0.34 MeV.     

A dimension formula for Bernoulli convolutions

We present a dynamical approach to the study of the singularity of infinitely convolved Bernoulli measuresv , for the golden section. We introducev as the transverse measure of the maximum entropy measure on the repelling set invariant for contracting maps of the square, the fat baker's transformation. Our approach strongly relies on the Markov structure of the underlying dynamical system. Indeed, if =golden mean, the fat baker's transformation has a very simple Markov coding. The ambiguity (of order two) of this coding, which appears when projecting on the line, due to passages for the central, overlapping zone, can be expressed by means of products of matrices (of order two). This product has a Markov distribution inherited by the Markov structure of the map. The dimension of the projected measure is therefore associated to the growth of this product; our dimension formula appears in a natural way as a version of the Furstenberg-Guivarch formula. Our technique provides an explicit dimension formula and, most important, provides a formalism well suited for the multifractal analysis of this measure, as we will show in a forthcoming paper.     

A formula for the relative entropy in chiral CFT

Letters in Mathematical Physics - We prove the QNEC on the Virasoro nets for a class of unitary states extending the coherent states, that is states obtained by applying an exponentiated stress...     

A resistance formula for coherent multi-barrier structures

Using the Landauer formula and the quantum S-matrix scattering theory, we derive a resistance formula for multi-barrier structure under phase coherent transmission condition. This formula shows that when the transport is coherent, the potential wells of the structure are just like conductors contributing to the overall resistance. And because the resistance formula is derived based on the scattering theory, the barrier resistance will change with the number of scattering centres (i.e. the number of barriers) in the structure.     

A formula for half-life of proton radioactivity

We present a formula for proton radioactivity half-lives of spherical proton emitters with the inclusion of the spectroscopic factor. The coefficients in the formula are calibrated with the available experimental data. As an input to calculate the half-life, the spectroscopic factor that characterizes the important information on nuclear structure should be obtained with a nuclear many-body approach. This formula is found to work quite well, and in better agreement with experimental measurements than other theoretical models. Therefore, it can be used as a powerful tool in the investigation of proton emission, in particular for experimentalists.     

A path-space formula for non-abelian gauge theories

A functional integral representation is obtained for a semigroup in an indefinite metric space giving the dynamics of a cutoff Yang-Mills theory in space-time dimensions greater than two. The Fadde'av-Popov formula is shown to arise as a stochastic integral in the Feynman gauge.     

A transformation formula for integrals over superfields

We give an intrinsic definition of an integral over superfields and show that there is no Jacobi determinant in the transformation formula for such integrals.