Renormalized Path Integral in Quantum Mechanics

We obtain direct, finite, descriptions of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description requires a modification to the Wiener measure on continuous paths that describes an unusual diffusion process wherein colliding particles occasionally stick together for a random interval of time before going their separate ways.Comment: 13 pgs, plain TEX fil

Disparity between the Programmatic Views and the User Perceptions of Mobile Apps

User perception in any mobile-app ecosystem, is represented as user ratings of apps. Unfortunately, the user ratings are often biased and do not reflect the actual usability of an app. To address the challenges associated with selection and ranking of apps, we need to use a comprehensive and holistic view about the behavior of an app. In this paper, we present and evaluate Trust based Rating and Ranking (TRR) approach. It relies solely on an apps' internal view that uses programmatic artifacts. We compute a trust tuple (Belief, Disbelief, Uncertainty - B, D, U) for each app based on the internal view and use it to rank the order apps offering similar functionality. Apps used for empirically evaluating the TRR approach are collected from the Google Play Store. Our experiments compare the TRR ranking with the user review-based ranking present in the Google Play Store. Although, there are disparities between the two rankings, a slightly deeper investigation indicates an underlying similarity between the two alternatives

Solitons in a Bilocal Field Theory

We obtain a bilocal classical field theory as the large $N$ limit of the chiral Gross--Neveu (or non--abelian Thirring) model. Exact classical solutions that describe topological solitons are obtained. It is shown that their mass spectrum agrees with the large $N$ limit of the spectrum of the chiral Gross--Neveu model.Comment: Tex, 18 pages, no figure

Relative volume of separable bipartite states

Every choice of an orthonormal frame in the d-dimensional Hilbert space of a system corresponds to one set of all mutually commuting density matrices or, equivalently, a classical statistical state space of the system; the quantum state space itself can thus be profitably viewed as an SU(d) orbit of classical state spaces, one for each orthonormal frame. We exploit this connection to study the relative volume of separable states of a bipartite quantum system. While the two-qubit case is studied in considerable analytic detail, for higher dimensional systems we fall back on Monte Carlo. Several new insights seem to emerge from our study.Comment: Essentially the published versio

Renormalized Contact Potential in Two Dimensions

We obtain for the attractive Dirac delta-function potential in two-dimensional quantum mechanics a renormalized formulation that avoids reference to a cutoff and running coupling constant. Dimensional transmutation is carried out before attempting to solve the system, and leads to an interesting eigenvalue problem in N-2 degrees of freedom (in the center of momentum frame) when there are N particles. The effective Hamiltonian for N-2 particles has a nonlocal attractive interaction, and the Schrodinger equation becomes an eigenvalue problem for the logarithm of this Hamiltonian. The 3-body case is examined in detail, and in this case a variational estimate of the ground-state energy is given.Comment: Plain Te

Atomic Compton profiles within different exchange-only theories

The Impulse Compton Profiles (CP's) J(q) and the - expectation values for some inert gas atoms (He-Kr) are computed and compared within the Harbola-Sahni (HS), Hartree-Fock(HF) theories and a Self Interaction Corrected (SIC) density functional model. The Compton profiles for excited states of Helium atom are also calculated. While the calculated CP's are found to generally agree, they differ slightly from one another for small values of the Compton parameter q and are in good agreement for large q values. The expectation values within the three theories are also found to be comparable. The HS formalism seem to mimic HF reasonably well in the momentum space, establishing the logical consistency of the former.Comment: 15 page