Computation on a Noiseless Quantum Code and Symmetrization

Let ${\cal H}$ be the state-space of a quantum computer coupled with the environment by a set of error operators spanning a Lie algebra ${\cal L}.$ Suppose ${\cal L}$ admits a noiseless quantum code i.e., a subspace ${\cal C}\subset{\cal H}$ annihilated by ${\cal L}.$ We show that a universal set of gates over $\cal C$ is obtained by any generic pair of ${\cal L}$-invariant gates. Such gates - if not available from the outset - can be obtained by resorting to a symmetrization with respect to the group generated by ${\cal L}.$ Any computation can then be performed completely within the coding decoherence-free subspace.Comment: One result added, to appear in Phys. Rev. A (RC) 4 pages LaTeX, no figure

Multiphonon decay of strong mode in quantum lattice

A nonperturbative theory of multiphonon anharmonic decay of strongly excited local mode is developed whereby the mode is considered classically and phonons, quantum mechanically. The decay rate of the mode is expressed via the negative frequency parts of the phonon pair correlation functions. In the case of two-phonon decay the later satisfy the linear integral equations while in the case of two- and more-phonon decay they satisfy the nonlinear integral equations. As a result, the processes mentioned differently depend on the mode amplitude A: two-phonon processes smoothly deminish if A tends to infinity while three- and more-phonon processes are fully switched-off at large amplitudes and they abruptly switch-on if the amplitude approaches the critical value. At that the decay rate gets rather high value (of the order of the mode quantum per period). The final stage of the relaxation is well described by the perturbation theory.Comment: 13 pages. submitted to Zeitschrift fur Physik B, to appear Vol.104, Dec. 199

The phase-space structure of the Klein-Gordon field

The formalism based on the equal-time Wigner function of the two-point correlation function for a quantized Klein--Gordon field is presented. The notion of the gauge-invariant Wigner transform is introduced and equations for the corresponding phase-space calculus are formulated. The equations of motion governing the Wigner function of the Klein--Gordon field are derived. It is shown that they lead to a relativistic transport equation with electric and magnetic forces and quantum corrections. The governing equations are much simpler than in the fermionic case which has been treated earlier. In addition the newly developed formalism is applied towards the description of spontaneous symmetry breakdown.Comment: 27 pages, LaTeX, UFTP 317/199

An alternative functional renormalization group approach to the single impurity Anderson model

We present an alternative functional renormalization group (fRG) approach to the single-impurity Anderson model at finite temperatures. Starting with the exact self-energy and interaction vertex of a small system ('core') containing a correlated site, we switch on the hybridization with a non-interacting bath in the fRG-flow and calculate spectra of the correlated site. Different truncations of the RG-flow-equations and choices of the core are compared and discussed. Furthermore we calculate the linear conductance and the magnetic susceptibility as functions of temperature and interaction strength. The signatures of Kondo physics arising in the flow are compared with numerical renormalization group results.Comment: 16 page

Universal aspects of non-equilibrium currents in a quantum dot

We study the electric current in the non-equilibrium Kondo model at zero magnetic field, using real-time perturbation theory in the Schwinger-Keldysh formulation. We show that the perturbative coefficients to all orders have a finite limit at large switch-on time (t_0 to minus infinity), and we give a prescription for general operators to give finite coefficients in this limit. We explain how this is related to the fact that the leads play the role of thermal baths and allow relaxation to occur and the steady state to form. This proves perturbatively that a steady state is reached in the Schwinger-Keldysh formulation, and specifies which operators correspond to quantities that have a well-defined value in the steady state. Then, we show that the steady state can be described by a special type of density matrix (related to Hershfield's conjecture for the particular example of the non-equilibrium Kondo model.) In the second part of the paper we perform a renormalization-group analysis of the perturbative series. We give a general argument that strongly suggests that the perturbative series of any average in the steady state satisfies the equilibrium Callan-Symanzik equations, and show in detail how it works to one-loop order for the electric current operator inside any average. We finally compute to two loops order the average of the electric current in the steady state, and perform a renormalization-group improvement. From this, we give a universal prescription, valid in the perturbative regime, for comparing the effect of the electric current to that of the temperature on the ``Kondo cloud''.Comment: 35 pages, 2 figures; v2: typos corrected, introduction and conclusion enhanced; v3: more discussion, published versio

Adiabatic Expansion for Metric Perturbation and the condition to solve the Gauge Problem for Gravitational Radiation Reaction Problem

We examine the adiabatic approximation in the study of a relativistic two-body problem with the gravitational radiation reaction. We recently pointed out that the usual metric perturbation scheme using a perturbation of the stress-energy tensor may not be appropriate for study of the dissipative dynamics of the bodies due to the radiation reaction. We recently proposed a possible approach to solve this problem with a linear black hole perturbation. This paper proposes a non-linear generalization of that method for a general application of this problem. We show that, under a specific gauge condition, the method actually allows us to avoid the gauge problem.Comment: accepted by Progress of Theoretical Physic