15 research outputs found
Universal asymptotic behavior in flow equations of dissipative systems
Based on two dissipative models, universal asymptotic behavior of flow
equations for Hamiltonians is found and discussed. Universal asymptotic
behavior only depends on fundamental bath properties but not on initial system
parameters, and the integro-differential equations possess an universal
attractor. The asymptotic flow of the Hamiltonian can be characterized by a
non-local differential equation which only depends on one parameter -
independent of the dissipative system or truncation scheme. Since the fixed
point Hamiltonian is trivial, the physical information is completely
transferred to the transformation of the observables. This yields a more stable
flow which is crucial for the numerical evaluation of correlation functions.
Furthermore, the low energy behavior of correlation functions is determined
analytically. The presented procedure can also be applied if relevant
perturbations are present as is demonstrated by evaluating dynamical
correlation functions for sub-Ohmic environments. It can further be generalized
to other dissipative systems.Comment: 15 pages, 9 figures; to appear in Phys. Rev.
Flow equation analysis of the anisotropic Kondo model
We use the new method of infinitesimal unitary transformations to calculate
zero temperature correlation functions in the strong-coupling phase of the
anisotropic Kondo model. We find the dynamics on all energy scales including
the crossover behaviour from weak to strong coupling. The integrable structure
of the Hamiltonian is not used in our approach. Our method should also be
useful in other strong-coupling models since few other analytical methods allow
the evaluation of their correlation functions on all energy scales.Comment: 4 pages RevTeX, 2 eps figures include
Nonperturbative Renormalization and the QCD Vacuum
We present a self consistent approach to Coulomb gauge Hamiltonian QCD which
allows one to relate single gluon spectral properties to the long range
behavior of the confining interaction. Nonperturbative renormalization is
discussed. The numerical results are in good agreement with phenomenological
and lattice forms of the static potential.Comment: 23 pages in RevTex, 4 postscript figure
Non-linear feedback effects in coupled Boson-Fermion systems
We address ourselves to a class of systems composed of two coupled subsystems
without any intra-subsystem interaction: itinerant Fermions and localized
Bosons on a lattice. Switching on an interaction between the two subsystems
leads to feedback effects which result in a rich dynamical structure in both of
them. Such feedback features are studied on the basis of the flow equation
technique - an infinite series of infinitesimal unitary transformations - which
leads to a gradual elimination of the inter-subsystem interaction. As a result
the two subsystems get decoupled but their renormalized kinetic energies become
mutually dependent on each other. Choosing for the inter - subsystem
interaction a charge exchange term (the Boson-Fermion model) the initially
localized Bosons acquire itinerancy through their dependence on the
renormalized Fermion dispersion. This latter evolves from a free particle
dispersion into one showing a pseudogap structure near the chemical potential.
Upon lowering the temperature both subsystems simultaneously enter a
macroscopic coherent quantum state. The Bosons become superfluid, exhibiting a
soundwave like dispersion while the Fermions develop a true gap in their
dispersion. The essential physical features described by this technique are
already contained in the renormalization of the kinetic terms in the respective
Hamiltonians of the two subsystems. The extra interaction terms resulting in
the process of iteration only strengthen this physics. We compare the results
with previous calculations based on selfconsistent perturbative approaches.Comment: 14 pages, 16 figures, accepted for publication in Phys. Rev.
Hole Dispersions for Antiferromagnetic Spin-1/2 Two-Leg Ladders by Self-Similar Continuous Unitary Transformations
The hole-doped antiferromagnetic spin-1/2 two-leg ladder is an important
model system for the high- superconductors based on cuprates. Using the
technique of self-similar continuous unitary transformations we derive
effective Hamiltonians for the charge motion in these ladders. The key
advantage of this technique is that it provides effective models explicitly in
the thermodynamic limit. A real space restriction of the generator of the
transformation allows us to explore the experimentally relevant parameter
space. From the effective Hamiltonians we calculate the dispersions for single
holes. Further calculations will enable the calculation of the interaction of
two holes so that a handle of Cooper pair formation is within reach.Comment: 16 pages, 26 figure
Asymptotic Freedom of Gluons in the Fock Space
Asymptotic freedom of gluons is described in terms of a family of scale-dependent renormalized Hamiltonian operators acting in the Fock space. The Hamiltonians are obtained by applying the renormalization group procedure for effective particles to quantum Yang-Mills theory
Renormalization group procedure for potential −g/r2
Schrödinger equation with potential −g/r2 exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at r=0. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of g. Keywords: Renormalization group procedure, Hamiltonian, Limit cycle, Asymptotic freedom, Triviality, Fixed point, Scale symmetry breaking, Quantum mechanic