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R. Kobes

Publications and source records attributed to R. Kobes.

At least 19 recordsLinked to original sources
arXiv2011

Geometrical entanglement of highly symmetric multipartite states and the Schmidt decomposition

In a previous paper we examined a geometric measure of entanglement based on the minimum distance between the entangled target state of interest and the space of unnormalized product states. Here we present a detailed study of this entanglement measure for target states with a large degree of symmetry. We obtain analytic solutions for the extrema of the distance function and solve for the Hessian to show that, up to the action of trivial symmetries, the solutions correspond to local minima of the distance function. In addition, we show that the conditions that determine the extremal solutions for general target states can be obtained directly by parametrizing the product states via their Schmidt decomposition.

quant-ph↗
arXiv2010

Weakly interacting Bose gases below the critical temperature

We consider a homogeneous non-ideal Bose gas at nonzero temperature in equilibrium below the critical temperature $T_C$ in the framework of finite temperature field theory. An algorithm is described in which a manageable subset of diagrams can be considered which, coupled with a self--consistent condition related to the minimization of the free energy, can be used to obtain physically reasonable results.

cond-mat.other↗
arXiv2010

Geometric measures of entanglement and the Schmidt decomposition

In the standard geometric approach, the entanglement of a pure state is $\sin^2θ$, where $θ$ is the angle between the entangled state and the closest separable state of products of normalised qubit states. We consider here a generalisation of this notion by considering separable states that consist of products of unnormalised states of different dimension. The distance between the target entangled state and the closest unnormalised product state can be interpreted as a measure of the entanglement of the target state. The components of the closest product state and its norm have an interpretation in terms of, respectively, the eigenvectors and eigenvalues of the reduced density matrices arising in the Schmidt decomposition of the state vector. For several cases where the target state has a large degree of symmetry, we solve the system of equations analytically, and look specifically at the limit where the number of qubits is large.

quant-ph↗
arXiv2007

Decoherence of a Single Qubit from Quantum Anomaly

We show via an explicit example that quantum anomalies can lead to decoherence of a single quantum qubit through phase relaxation. The anomaly causes the Hamiltonian to develop a non-self-adjoint piece due to the non-invariance of the domain of the Hamiltonian under symmetry transformation. The resulting decoherence originates completely from the dynamics of the system itself and not, as usually considered, from interactions with the environment.

quant-ph↗
arXiv2007

Geometric measures of entanglement and the Schmidt decomposition

In the standard geometric approach to a measure of entanglement of a pure state, $\sin^2θ$ is used, where $θ$ is the angle between the state to the closest separable state of products of normalized qubit states. We consider here a generalization of this notion to separable states consisting of products of unnormalized states of different dimension. In so doing, the entanglement measure $\sin^2θ$ is found to have an interpretation as the distance between the state to the closest separable state. We also find the components of the closest separable state and its norm have an interpretation in terms of, respectively, the eigenvectors and eigenvalues of the reduced density matrices arising in the Schmidt decomposition of the state vector.

quant-ph↗
arXiv2006

The Dynamics of Entanglement in the Adiabatic Search and Deutsch Algorithms

The goal of this paper is to study the effect of entanglement on the running time of a quantum computation. Adiabatic quantum computation is suited to this kind of study, since it allows us to explicitly calculate the time evolution of the entanglement throughout the calculation. On the other hand however, the adiabatic formalism makes it impossible to study the roles of entanglement and fidelity separately, which means that results have to be interpreted carefully. We study two algorithms: the search algorithm and the Deutsch-Jozsa algorithm. We find some evidence that entanglement can be considered a resource in quantum computation.

quant-ph↗
arXiv2005

Energy Flow in Acoustic Black Holes

We present the results of an analysis of superradiant energy flow due to scalar fields incident on an acoustic black hole. In addition to providing independent confirmation of the recent results in [5], we determine in detail the profile of energy flow everywhere outside the horizon. We confirm explicitly that in a suitable frame the energy flow is inward at the horizon and outward at infinity, as expected on physical grounds.

gr-qc↗
arXiv2004

POVM optimization of classical correlations

We study the problem of optimization over positive valued-operator measure to extract classical correlation in a bipartite quantum system. The proposed method is applied to binary states only. Moreover, to illustrate this method, an explicit example is studied in details.

quant-ph↗
arXiv2003

A new adiabatic quantum search algorithm

We present a new adiabatic quantum algorithm for searching over structured databases. The new algorithm is optimized using a simplified complexity analysis.

quant-ph↗
arXiv2002

Scattering amplitudes at finite temperature

We present a simple set of rules for obtaining the imaginary part of a self energy diagram at finite temperature in terms of diagrams that correspond to physical scattering amplitudes.

hep-ph↗
arXiv2001

Non-linear Fractal Interpolating Functions

We consider two non-linear generalizations of fractal interpolating functions generated from iterated function systems. The first corresponds to fitting data using a Kth-order polynomial, while the second relates to the freedom of adding certain arbitrary functions. An escape-time algorithm that can be used for such systems to generate fractal images like those associated with Julia or Mandelbrot sets is also described.

nlin.CD↗
arXiv2001

Chapman-Enskog expansion of the Boltzmann equation and its diagrammatic interpretation

We perform a Chapman-Enskog expansion of the Boltzmann equation keeping up to quadratic contributions. We obtain a generalized nonlinear Kubo formula, and a set of integral equations which resum ladder and extended ladder diagrams. We show that these two equations have exactly the same structure, and thus provide a diagrammatic interpretation of the Chapman-Enskog expansion of the Boltzmann equation, up to quadratic order.

hep-ph↗
arXiv2001

Infrared behaviour of the pressure in gϕ^3 theory in 6 dimensions

In an earlier paper Almeida and Frenkel considered the calculation of the pressure in gϕ^3 theory in 6 dimensions via the Schwinger--Dyson equation. They found, under certain approximations, that a finite result ensues in the infrared limit. We find this conclusion to remain true with certain variations of these approximations, suggesting the finiteness of the result to be fairly robust.

hep-ph↗
arXiv2001

A Diagrammatic Interpretation of the Boltzmann Equation

We study nonlinear response in weakly coupled nonequilibrium $ϕ^4$ theory in the context of both classical transport theory and real time quantum field theory, based on a generalized Kubo formula which we derive. A novel connection between these two approaches is established which provides a diagrammatic interpretation of the Boltzmann equation.

hep-ph↗
arXiv2001

Equilibration in an Interacting Field Theory

We use a combination of perturbation theory and numerical techniques to study the equilibration of two interacting fields which are initially at thermal equilibrium at different temperatures. Using standard rules of quantum field theory, we examine the master equations that describe the time evolution of the distribution functions for the two coupled systems. By making a few reasonable assumptions we reduce the resulting coupled integral/differential equations to a pair of differential equations that can be solved numerically. Our results show with good accuracy how these coupled systems approach a common equilibrium temperature.

hep-ph↗
arXiv2001

Nonlinear Response from Transport Theory and Quantum Field Theory at Finite Temperature

We study nonlinear response in weakly coupled hot $ϕ^4$ theory. We obtain an expression for a quadratic shear viscous response coefficient using two different formalisms: transport theory and response theory. The transport theory calculation is carried out by assuming a local equilibrium form for the distribution function and expanding in the gradient of the local four dimensional velocity field. By doing a gradient expansion on the Boltzmann equation we obtain a hierarchy of equations for the coefficients of this expansion.To do the response theory calculation we use Zubrave's techniques in nonequilibrium statistical mechanics to derive a generalized Kubo formula. Using this formula allows us to obtain the quadratic shear viscous response from the three-point retarded green function of the viscous shear stress tensor. We use the closed time path formalism of real time finite temperature field theoryto show that this three-point function can be calculated using equilibrium quantum field theory by writing it as an integral equation involving a four-point vertex. This four-point vertex can in turn be obtained from an integral equation which represents the resummation of an infinite series of ladder and extended-ladder diagrams.The connection between transport theory and response theory is made when we show that the integral equation for this four-point vertex has exactly the same form as the equation obtained from the Boltzmann equation for the coefficient of the quadratic term of the gradient expansion of the distribution function.

hep-ph↗
arXiv2000

A Relationship Between Parametric Resonance and Chaos

In this paper we study two types of exponential instability -- parametric resonance and chaos. We show that a given equation may produce chaos or parametric resonance, depending how the problem is defined. In so doing we establish a relationship between the Floquet indices (associated with parametric resonance) and Lyapunov exponents (associated with chaos).

nlin.CD↗