Universal Reduction of Effective Coordination Number in the Quasi-One-Dimensional Ising Model

Critical temperature of quasi-one-dimensional general-spin Ising ferromagnets is investigated by means of the cluster Monte Carlo method performed on infinite-length strips, L times infty or L times L times infty. We find that in the weak interchain coupling regime the critical temperature as a function of the interchain coupling is well-described by a chain mean-field formula with a reduced effective coordination number, as the quantum Heisenberg antiferromagnets recently reported by Yasuda et al. [Phys. Rev. Lett. 94, 217201 (2005)]. It is also confirmed that the effective coordination number is independent of the spin size. We show that in the weak interchain coupling limit the effective coordination number is, irrespective of the spin size, rigorously given by the quantum critical point of a spin-1/2 transverse-field Ising model.Comment: 12 pages, 6 figures, minor modifications, final version published in Phys. Rev.

Sequential minimal optimization for quantum-classical hybrid algorithms

We propose a sequential minimal optimization method for quantum-classical hybrid algorithms, which converges faster, is robust against statistical error, and is hyperparameter-free. Specifically, the optimization problem of the parameterized quantum circuits is divided into solvable subproblems by considering only a subset of the parameters. In fact, if we choose a single parameter, the cost function becomes a simple sine curve with period $2\pi$, and hence we can exactly minimize with respect to the chosen parameter. Furthermore, even in general cases, the cost function is given by a simple sum of trigonometric functions with certain periods and hence can be minimized by using a classical computer. By repeatedly performing this procedure, we can optimize the parameterized quantum circuits so that the cost function becomes as small as possible. We perform numerical simulations and compare the proposed method with existing gradient-free and gradient-based optimization algorithms. We find that the proposed method substantially outperforms the existing optimization algorithms and converges to a solution almost independent of the initial choice of the parameters. This accelerates almost all quantum-classical hybrid algorithms readily and would be a key tool for harnessing near-term quantum devices.Comment: 11 pages, 4 figure

On the differential geometry of curves in Minkowski space

We discuss some aspects of the differential geometry of curves in Minkowski space. We establish the Serret-Frenet equations in Minkowski space and use them to give a very simple proof of the fundamental theorem of curves in Minkowski space. We also state and prove two other theorems which represent Minkowskian versions of a very known theorem of the differential geometry of curves in tridimensional Euclidean space. We discuss the general solution for torsionless paths in Minkowki space. We then apply the four-dimensional Serret-Frenet equations to describe the motion of a charged test particle in a constant and uniform electromagnetic field and show how the curvature and the torsions of the four-dimensional path of the particle contain information on the electromagnetic field acting on the particle.Comment: 10 pages. Typeset using REVTE

Quantum phase shift and neutrino oscillations in a stationary, weak gravitational field

A new method based on Synge's world function is developed for determining within the WKB approximation the gravitationally induced quantum phase shift of a particle propagating in a stationary spacetime. This method avoids any calculation of geodesics. A detailed treatment is given for relativistic particles within the weak field, linear approximation of any metric theory. The method is applied to the calculation of the oscillation terms governing the interference of neutrinos considered as a superposition of two eigenstates having different masses. It is shown that the neutrino oscillations are not sensitive to the gravitomagnetic components of the metric as long as the spin contributions can be ignored. Explicit calculations are performed when the source of the field is a spherical, homogeneous body. A comparison is made with previous results obtained in Schwarzschild spacetime.Comment: 14 pages, no figure. Enlarged version; added references. In the Schwarzschild case, our results on the non-radial propagation are compared with the previous work

Energy Contents of Gravitational Waves in Teleparallel Gravity

The conserved quantities, that are, gravitational energy-momentum and its relevant quantities are investigated for cylindrical and spherical gravitational waves in the framework of teleparallel equivalent of General Relativity using the Hamiltonian approach. For both cylindrical and spherical gravitational waves, we obtain definite energy and constant momentum. The constant momentum shows consistency with the results available in General Relativity and teleparallel gravity. The angular momentum for cylindrical and spherical gravitational waves also turn out to be constant. Further, we evaluate their gravitational energy-momentum fluxes and gravitational pressure.Comment: 14 pages, accepted for publication in Mod. Phys. Lett.

Mode-sum regularization of the scalar self-force: Formulation in terms of a tetrad decomposition of the singular field

We examine the motion in Schwarzschild spacetime of a point particle endowed with a scalar charge. The particle produces a retarded scalar field which interacts with the particle and influences its motion via the action of a self-force. We exploit the spherical symmetry of the Schwarzschild spacetime and decompose the scalar field in spherical-harmonic modes. Although each mode is bounded at the position of the particle, a mode-sum evaluation of the self-force requires regularization because the sum does not converge: the retarded field is infinite at the position of the particle. The regularization procedure involves the computation of regularization parameters, which are obtained from a mode decomposition of the Detweiler-Whiting singular field; these are subtracted from the modes of the retarded field, and the result is a mode-sum that converges to the actual self-force. We present such a computation in this paper. There are two main aspects of our work that are new. First, we define the regularization parameters as scalar quantities by referring them to a tetrad decomposition of the singular field. Second, we calculate four sets of regularization parameters (denoted schematically by A, B, C, and D) instead of the usual three (A, B, and C). As proof of principle that our methods are reliable, we calculate the self-force acting on a scalar charge in circular motion around a Schwarzschild black hole, and compare our answers with those recorded in the literature.Comment: 38 pages, 2 figure

The Problem of Inertia in Friedmann Universes

In this paper we study the origin of inertia in a curved spacetime, particularly the spatially flat, open and closed Friedmann universes. This is done using Sciama's law of inertial induction, which is based on Mach's principle, and expresses the analogy between the retarded far fields of electrodynamics and those of gravitation. After obtaining covariant expressions for electromagnetic fields due to an accelerating point charge in Friedmann models, we adopt Sciama's law to obtain the inertial force on an accelerating mass $m$ by integrating over the contributions from all the matter in the universe. The resulting inertial force has the form $F = -kma$, where $k < 1$ depends on the choice of the cosmological parameters such as $\Omega_{M}$, $\Omega_{\Lambda}$, and $\Omega_{R}$ and is also red-shift dependent.Comment: 10 page

Quantum vacuum effects as generalized f(R) gravity. Application to stars

It is assumed that, for weak spacetime curvature, the main gravitational effect of the quantum vacuum stress-energy corresponds to adding two terms to the Einstein-Hilbert action, proportional to the square of the curvature scalar and to the contraction of two Ricci tensors, respectively. It is shown that compatibility with terrestrial and solar systems observaction implies that the square roorts of the coefficients of these terms should be either a few millimeters or a few hundred meters. It is shown that the vacuum contribution increase the stability of white dwarfs.Comment: GEneralizes and improves previous versio

H-theorem for classical matter around a black hole

We propose a classical solution for the kinetic description of matter falling into a black hole, which permits to evaluate both the kinetic entropy and the entropy production rate of classical infalling matter at the event horizon. The formulation is based on a relativistic kinetic description for classical particles in the presence of an event horizon. An H-theorem is established which holds for arbitrary models of black holes and is valid also in the presence of contracting event horizons