Radhika Vathsan

Einstein's Recoiling Slit Experiment, Complementarity and Uncertainty

We analyze Einsteins recoiling slit experiment and point out that the inevitable entanglement between the particle and the recoiling slit was not part of Bohrs reply. We show that if this entanglement is taken into account, one can provide a simpler answer to Einstein. We also derive the Englert-Greenberger-Yasin duality relation from the entanglement between the particle and the recoiling slit. In addition, we show that the Englert-Greenberger-Yasin duality relation can also be thought of as a consequence of the sum uncertainty relation for certain observables of the recoiling slit. Thus, the uncertainty relations and entanglement are both an integral part of the which-way detection process. Quanta 2013; 2: 58–65.

Stable solitons in field theory models for tachyon condensation

We study soliton solutions in scalar field theory with a variety of unbounded potentials. A subset of these potentials have Gaussian lump solutions and their fluctuation spectrum is governed by the harmonic oscillator problem. These lumps are unstable with one tachyonic mode. Soliton solutions in several other classes of potentials are stable and are of kink type. The problem of the stability of these solutions is related to a supersymmetric quantum mechanics problem. The fluctuation spectrum is not equispaced and does not contain any tachyonic mode. The lowest energy mode is the massless Goldstone mode which restores broken translation invariance.

Classical Many-particle Clusters in Two Dimensions

We report on a study of a classical, finite system of confined particles in two dimensions with a two-body repulsive interaction. We first develop a simple analytical method for obtaining equilibrium configurations and energies for a few particles. When the confinement is harmonic, we prove that the first transition from a single shell occurs when the number of particles changes from five to six. The shell structure in the case of an arbitrary number of particles is shown to be independent of the strength of the interaction and dependent only on its functional form. It is also found to be independent of the magnetic field strength when this is included. We further study the effect of the functional form of the confinement potential on the shell structure. Finally, we report some interesting results obtained when a three-body interaction is included, albeit in a particular model.

Introduction to Quantum Physics and Information Processing

An Elementary Guide to the State of the Art in the Quantum Information Field Introduction to Quantum Physics and Information Processing guides beginners in understanding the current state of research in the novel, interdisciplinary area of quantum information. Suitable for undergraduate and beginning graduate students in physics, mathematics, or engineering, the book goes deep into issues of quantum theory without raising the technical level too much. The text begins with the basics of quantum mechanics required to understand how two-level systems are used as qubits. It goes on to show how quantum properties are exploited in devising algorithms for problems that are more efficient than the classical counterpart. It then explores more sophisticated notions that form the backbone of quantum information theory. Requiring no background in quantum physics, this text prepares readers to follow more advanced books and research material in this rapidly growing field. Examples, detailed discussions, exercises, and problems facilitate a thorough, real-world understanding of quantum information.

A note on fermion and gauge couplings in field theory models for tachyon condensation

Abstract We study soliton solutions in supersymmetric scalar field theory with a class of potentials. We study both bosonic and fermionic zero-modes around the soliton solution. We study two possible couplings of gauge fields to these models. While the Born–Infeld like coupling has one normalizable mode (the zero mode), the other kind of coupling has no normalizable modes. We show that quantum mechanical problem which determines the spectrum of fluctuation modes of the scalar, fermion and the gauge field is identical. We also show that only the lowest lying mode, i.e., the zero mode, is normalizable and the rest of the spectrum is continuous.

ASPECTS OF COMPLEMENTARITY AND UNCERTAINTY

The two-slit experiment with quantum particles provides many insights into the behaviour of quantum mechanics, including Bohrs complementarity principle. Here we analyze Einsteins recoiling slit version of the experiment and show how the inevitable entanglement between the particle and the recoiling slit as a which-way detector is responsible for complementarity. We derive the Englert-Greenberger-Yasin duality from this entanglement, which can also be thought of as a consequence of sum-uncertainty relations between certain complementary observables of the recoiling slit. Thus, entanglement is an integral part of the which-way detection process, and so is uncertainty, though in a completely different way from that envisaged by Bohr and Einstein.

REDUCTION OF ANYONS TO ONE DIMENSION AND CALOGERO–SUTHERLAND-TYPE MODELS

The two-dimensional anyon system, when reduced to one dimension, yields models related to the Calogero–Sutherland model. One such reduction leads to a new model with a class of exact solutions. This model is one of a family of models obtained upon dimensional reduction of spherically symmetric models in arbitrary dimensions.

Remarks on the quantization of gauge theories

The methods of reduced phase space quantization and Dirac quantization are examined in a simple gauge theory. It is pointed out that care needs to be exercised in implementing the reduced phase space quantization method properly.