arXiv subjects

Ken-Ichi Aoki

Publications and source records attributed to Ken-Ichi Aoki.

30 records · Page 2Linked to original sources

arXiv2003

Nonperturbative renormalization-group approach for quantum dissipative systems

We analyze the dissipative quantum tunneling in the Caldeira-Leggett model by the nonperturbative renormalization-group method. We classify the dissipation effects by introducing the notion of effective cutoffs. We calculate the localization susceptibility to evaluate the critical dissipation for the quantum-classical transition. Our results are consistent with previous semiclassical arguments, but give considerably larger critical dissipation.

quant-ph↗

arXiv2002

Non-Perturbative Renormalization Group Analysis in Quantum Mechanics

We analyze quantum mechanical systems using the non-perturbative renormalization group (NPRG). The NPRG method enables us to calculate quantum corrections systematically and is very effective for studying non-perturbative dynamics. We start with anharmonic oscillators and proceed to asymmetric double well potentials, supersymmetric quantum mechanics and many particle systems.

quant-ph↗

arXiv2000

Time of arrival through interacting environments: Tunneling processes

We discuss the propagation of wave packets through interacting environments. Such environments generally modify the dispersion relation or shape of the wave function. To study such effects in detail, we define the distribution function P_{X}(T), which describes the arrival time T of a packet at a detector located at point X. We calculate P_{X}(T) for wave packets traveling through a tunneling barrier and find that our results actually explain recent experiments. We compare our results with Nelson's stochastic interpretation of quantum mechanics and resolve a paradox previously apparent in Nelson's viewpoint about the tunneling time.

quant-ph↗

arXiv2000

Scheme Dependence of the Wilsonian Effective Action and Sharp Cutoff Limit of the Flow Equation

The cutoff scheme dependence in the several formulations of the Exact Renormalization Group (ERG) is investigated. It is shown that the cutoff scheme dependence of the Wilsonian effective action is regarded as a certain coordinate transformation on the theory space. From this observation the Wilsonian effective actions are found to suffer from strong dependence on the schemes even in the infra-red asymptotic region for massive theories. However there is no such scheme dependence in the one particle irreducible parts of them, which is called the effective average actions. We also derive the explicit form of the Polchinski RG equation in the sharp cutoff limit. Finally this equation is shown to be identical with the Wegner-Houghton RG equation.

hep-th↗

arXiv2000

Non-ladder Extended Renormalization Group Analysis of the Dynamical Chiral Symmetry Breaking

The order parameters of dynamical chiral symmetry breaking in QCD, the dynamical mass of quarks and the chiral condensates, are evaluated by numerically solving the Non-Perturbative Renormalization Group (NPRG) equations. We employ an approximation scheme beyond ``the ladder'', that is, beyond the (improved) ladder Schwinger-Dyson equations. The chiral condensates are enhanced compared with the ladder ones, which is phenomenologically favorable. The gauge dependence of the order parameters is fairly reduced in this scheme.

hep-th↗

arXiv1999

Analysis of the Wilsonian Effective Potentials in Dynamical Chiral Symmetry Breaking

The non-perturbative renormalization group equation for the Wilsonian effective potential is given in a certain simple approximation scheme in order to study chiral symmetry breaking phenomena dynamically induced by strong gauge interactions. The evolving effective potential is found to be non-analytic in infrared, which indicates spontaneous generation of the fermion mass. It is also shown that the renormalization group equation gives the identical effective fermion mass with that obtained by solving the Schwinger-Dyson equation in the (improved) ladder approximation. Moreover introduction of the collective field corresponding to the fermion composite into the theory space is found to offer an efficient method to evaluate the order parameters; the dynamical mass and the chiral condensate. The relation between the renormalization group equation incorporating the collective field and the Schwinger-Dyson equation is also clarified.

hep-th↗

arXiv1999

Wilson Renormalization Group Equations for the Critical Dynamics of Chiral Symmetry

The critical dynamics of the chiral symmetry breaking induced by gauge interaction is examined in the Wilson renormalization group framework in comparison with the Schwinger-Dyson approach. We derive the beta functions for the four-fermi couplings in the sharp cutoff renormalzation group scheme, from which the critical couplings and the anomalous dimensions of the fermion composite operators near criticality are immediately obtained. It is also shown that the beta functions lead to the same critical behavior found by solving the so-called ladder Schwinger-Dyson equation, if we restrict the radiative corrections to a certain limited type.

hep-th↗

arXiv1998

Non-Perturbative Renormalization Group and Quantum Tunnelling

The non-perturbative renormalization group (NPRG) is applied to analysis of tunnelling in quantum mechanics. The vacuum energy and the energy gap of anharmonic oscillators are evaluated by solving the local potential approximated Wegner-Houghton equation (LPA W-H eqn.). We find that our results are very good in a strong coupling region, but not in a very weak coupling region, where the dilute gas instanton calculation works very well. So it seems that in analysis of quantum tunnelling, the dilute gas instanton and LPA W-H eqn. play complementary roles to each other. We also analyze the supersymmetric quantum mechanics and see if the dynamical supersymmetry (SUSY) breaking is described by NPRG method.

hep-th↗

arXiv1998

Rapidly Converging Truncation Scheme of the Exact Renormalization Group

The truncation scheme dependence of the exact renormalization group equations is investigated for scalar field theories in three dimensions. The exponents are numerically estimated to the next-to-leading order of the derivative expansion. It is found that the convergence property in various truncations in the number of powers of the fields is remarkably improved if the expansion is made around the minimum of the effective potential. It is also shown that this truncation scheme is suitable for evaluation of infrared effective potentials. The physical interpretation of this improvement is discussed by considering O(N) symmetric scalar theories in the large-N limit.

hep-th↗

arXiv1997

Non-perturbative Renormalization Group Approach to Dynamical Chiral Symmetry Breaking in Gauge Theories

We analyze the dynamical chiral symmetry breaking in gauge theories solely by the non-perturbative renormalization group, without recourse to the Schwinger-Dyson method. First, we briefly review the basic notions and formulation, and clarify its great feature that it gives a systematic approximation scheme without any divergent series nor serious gauge dependence, compared to other perturbative and non-perturbative methods. Then we apply this new method to QED and QCD to find that our lowest level approximation improves the ladder Schwinger-Dyson equation results in a gauge independent way. We get the chiral phase structures and the critical exponents in the fixed gauge coupling analysis, and also calculate the chiral condensates in case of running QCD.

hep-ph↗

arXiv1997

Non-Perturbative Renormalization Group Analysis of the Chiral Critical Behaviors in QED

We study the chiral critical behaviors of QED by using Non-Perturbative Renormalization Group (NPRG). Taking account of the non-ladder contributions, our flow equations are free from the gauge parameter ($α$) dependence. We clarify the chiral phase structure, and calculate the anomalous dimension of $\barψψ$, which is enhanced compared to the ladder approximation. We find that the cutoff scheme dependence of the physical results is very small.

hep-ph↗

arXiv1996

The effectiveness of the local potential approximation in the Wegner-Houghton renormalization group

The non-perturbative Wegner-Houghton renormalization group is analyzed by the local potential approximation in O(N) scalar theories in d-dimensions $(3\leq d\leq 4)$. The leading critical exponents νare calculated in order to investigate the effectiveness of the local potential approximation by comparing them with the other non-perturbative methods. We show analytically that the local potential approximation gives the exact exponents up to $O(ε)$ in ε-expansion and the leading in 1/N-expansion. We claim that this approximation offers fairly accurate results in the whole range of the parameter space of N and d. It is a great advantage of our method that no diverging expansions appear in the procedure.

hep-ph↗