Towards a quantum Hall effect for atoms using electric fields

An atomic analogue of Landau quantization based on the Aharonov-Casher (AC) interaction is developed. The effect provides a first step towards an atomic quantum Hall system using electric fields, which may be realized in a Bose-Einstein condensate

Classical and Quantum Interaction of the Dipole

A unified and fully relativistic treatment of the interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is given. New forces on the particle due to the combined effect of electric and magnetic dipoles are obtained. Four new experiments are proposed, three of which would observe topological phase shifts.Comment: 10 pages, Latex/Revtex. Some minor errors have been correcte

Axiomatic Holonomy Maps and Generalized Yang-Mills Moduli Space

This article is a follow-up of ``Holonomy and Path Structures in General Relativity and Yang-Mills Theory" by Barrett, J. W. (Int.J.Theor.Phys., vol.30, No.9, 1991). Its main goal is to provide an alternative proof of this part of the reconstruction theorem which concerns the existence of a connection. A construction of connection 1-form is presented. The formula expressing the local coefficients of connection in terms of the holonomy map is obtained as an immediate consequence of that construction. Thus the derived formula coincides with that used in "On Loop Space Formulation of Gauge Theories" by Chan, H.-M., Scharbach, P. and Tsou S.T. (Ann.Phys., vol.167, 454-472, 1986). The reconstruction and representation theorems form a generalization of the fact that the pointed configuration space of the classical Yang-Mills theory is equivalent to the set of all holonomy maps. The point of this generalization is that there is a one-to-one correspondence not only between the holonomy maps and the orbits in the space of connections, but also between all maps from the loop space on $M$ to group $G$ fulfilling some axioms and all possible equivalence classes of $P(M,G)$ bundles with connection, where the equivalence relation is defined by bundle isomorphism in a natural way.Comment: amslatex, 7 pages, no figure

Gravitational Phase Operator and Cosmic Strings

A quantum equivalence principle is formulated by means of a gravitational phase operator which is an element of the Poincare group. This is applied to the spinning cosmic string which suggests that it may (but not necessarily) contain gravitational torsion. A new exact solution of the Einstein- Cartan-Sciama-Kibble equations for the gravitational field with torsion is obtained everywhere for a cosmic string with uniform energy density, spin density and flux. A novel effect due to the quantized gravitational field of the cosmic string on the wave function of a particle outside the string is used to argue that spacetime points are not meaningful in quantum gravity.Comment: 22 pages, to be published Phys. Rev. D. Some minor changes have been made and a reference has been added to the paper of D.V. Gal'tsov and P.S. Letelier, Phys. Rev. D 47 (1993) 4273, which first contained the metric (2.2) external to the cosmic string. The present paper extends this solution to a regular solution inside the string as wel

Topology, Locality, and Aharonov-Bohm Effect with Neutrons

Recent neutron interferometry experiments have been interpreted as demonstrating a new topological phenomenon similar in principle to the usual Aharonov-Bohm (AB) effect, but with the neutron's magnetic moment replacing the electron's charge. We show that the new phenomenon, called Scalar AB (SAB) effect, follows from an ordinary local interaction, contrary to the usual AB effect, and we argue that the SAB effect is not a topological effect by any useful definition. We find that SAB actually measures an apparently novel spin autocorrelation whose operator equations of motion contain the local torque in the magnetic field. We note that the same remarks apply to the Aharonov-Casher effect.Comment: 9 page

Action principle formulation for motion of extended bodies in General Relativity

We present an action principle formulation for the study of motion of an extended body in General Relativity in the limit of weak gravitational field. This gives the classical equations of motion for multipole moments of arbitrary order coupling to the gravitational field. In particular, a new force due to the octupole moment is obtained. The action also yields the gravitationally induced phase shifts in quantum interference experiments due to the coupling of all multipole moments.Comment: Revised version derives Octupole moment force. Some clarifications and a reference added. To appear in Phys. Rev.

On the measurement problem for a two-level quantum system

A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes is developed. In this approach the Schrodinger evolution of a quantum system is a geodesic motion on the space of states of the system furnished with an appropriate Riemannian metric. The measuring device is modeled by a perturbation of the metric. The process of measurement is identified with a geodesic motion of state of the system in the perturbed metric. Under the assumption of random fluctuations of the perturbed metric, the Born rule for probabilities of collapse is derived. The approach is applied to a two-level quantum system to obtain a simple geometric interpretation of quantum commutators, the uncertainty principle and Planck's constant. In light of this, a lucid analysis of the double-slit experiment with collapse and an experiment on a pair of entangled particles is presented.Comment: for related papers, see http://www.uwc.edu/dept/math/faculty/kryukov

On the Interpretation of Energy as the Rate of Quantum Computation

Over the last few decades, developments in the physical limits of computing and quantum computing have increasingly taught us that it can be helpful to think about physics itself in computational terms. For example, work over the last decade has shown that the energy of a quantum system limits the rate at which it can perform significant computational operations, and suggests that we might validly interpret energy as in fact being the speed at which a physical system is "computing," in some appropriate sense of the word. In this paper, we explore the precise nature of this connection. Elementary results in quantum theory show that the Hamiltonian energy of any quantum system corresponds exactly to the angular velocity of state-vector rotation (defined in a certain natural way) in Hilbert space, and also to the rate at which the state-vector's components (in any basis) sweep out area in the complex plane. The total angle traversed (or area swept out) corresponds to the action of the Hamiltonian operator along the trajectory, and we can also consider it to be a measure of the "amount of computational effort exerted" by the system, or effort for short. For any specific quantum or classical computational operation, we can (at least in principle) calculate its difficulty, defined as the minimum effort required to perform that operation on a worst-case input state, and this in turn determines the minimum time required for quantum systems to carry out that operation on worst-case input states of a given energy. As examples, we calculate the difficulty of some basic 1-bit and n-bit quantum and classical operations in an simple unconstrained scenario.Comment: Revised to address reviewer comments. Corrects an error relating to time-ordering, adds some additional references and discussion, shortened in a few places. Figures now incorporated into tex

Global Topology and Local Violation of Discrete Symmetries

Cosmological models that are locally consistent with general relativity and the standard model in which an object transported around the universe undergoes P, C and CP transformations, are constructed. This leads to generalization of the gauge fields that describe electro-weak and strong interactions by enlarging the gauge groups to include anti-unitary transformations. Gedanken experiments show that if all interactions obey Einstein causality then P, C and CP cannot be violated in these models. But another model, which would violate charge superselection rule even for an isolated system, is allowed. It is suggested that the fundamental physical laws must have these discrete symmetries which are broken spontaneously, or they must be non causal.Comment: 12 pages, 1 figure, latex, Revtex. Charge conjugation which is physically implemented in a cosmology with the appropriate topology is described in more detail. Some minor errors are corrected. Shortened to meet the page limit of Physical Review Letters to which this paper was submitte

Continuous Time-Dependent Measurements: Quantum Anti-Zeno Paradox with Applications

We derive differential equations for the modified Feynman propagator and for the density operator describing time-dependent measurements or histories continuous in time. We obtain an exact series solution and discuss its applications. Suppose the system is initially in a state with density operator $\rho(0)$ and the projection operator $E(t) = U(t) E U^\dagger(t)$ is measured continuously from $t = 0$ to $T$, where $E$ is a projector obeying $E\rho(0) E = \rho(0)$ and $U(t)$ a unitary operator obeying $U(0) = 1$ and some smoothness conditions in $t$. Then the probability of always finding $E(t) = 1$ from $t = 0$ to $T$ is unity. Generically $E(T) \neq E$ and the watched system is sure to change its state, which is the anti-Zeno paradox noted by us recently. Our results valid for projectors of arbitrary rank generalize those obtained by Anandan and Aharonov for projectors of unit rank.Comment: 16 pages, latex; new material and references adde