Non-Abelian statistics of vortices with non-Abelian Dirac fermions

We extend our previous analysis on the exchange statistics of vortices having a single Dirac fermion trapped in each core, to the case where vortices trap two Dirac fermions with U(2) symmetry. Such a system of vortices with non-Abelian Dirac fermions appears in color superconductors at extremely high densities, and in supersymmetric QCD. We show that the exchange of two vortices having doublet Dirac fermions in each core is expressed by non-Abelian representations of a braid group, which is explicitly verified in the matrix representation of the exchange operators when the number of vortices is up to four. We find that the result contains the matrices previously obtained for the vortices with a single Dirac fermion in each core as a special case. The whole braid group does not immediately imply non-Abelian statistics of identical particles because it also contains exchanges between vortices with different numbers of Dirac fermions. However, we find that it does contain, as its subgroup, a genuine non-Abelian statistics for the exchange of the identical particles, that is, vortices with the same number of Dirac fermions. This result is surprising compared with conventional understanding because all Dirac fermions are defined locally at each vortex, unlike the case of Majorana fermions for which Dirac fermions are defined non-locally by Majorana fermions located at two spatially separated vortices.Comment: 32 pages, no figures, v3: published versio

Dynamical Chiral Symmetry Breaking on the Light Front.II. The Nambu--Jona-Lasinio Model

An investigation of dynamical chiral symmetry breaking on the light front is made in the Nambu--Jona-Lasinio model with one flavor and N colors. Analysis of the model suffers from extraordinary complexity due to the existence of a "fermionic constraint," i.e., a constraint equation for the bad spinor component. However, to solve this constraint is of special importance. In classical theory, we can exactly solve it and then explicitly check the property of ``light-front chiral transformation.'' In quantum theory, we introduce a bilocal formulation to solve the fermionic constraint by the 1/N expansion. Systematic 1/N expansion of the fermion bilocal operator is realized by the boson expansion method. The leading (bilocal) fermionic constraint becomes a gap equation for a chiral condensate and thus if we choose a nontrivial solution of the gap equation, we are in the broken phase. As a result of the nonzero chiral condensate, we find unusual chiral transformation of fields and nonvanishing of the light-front chiral charge. A leading order eigenvalue equation for a single bosonic state is equivalent to a leading order fermion-antifermion bound-state equation. We analytically solve it for scalar and pseudoscalar mesons and obtain their light-cone wavefunctions and masses. All of the results are entirely consistent with those of our previous analysis on the chiral Yukawa model.Comment: 23 pages, REVTEX, the version to be published in Phys.Rev.D; Some clarifications in discussion of the LC wavefunctions adde

Chiral Condensate and Short-Time Evolution of QCD(1+1) on the Light-Cone

Chiral condensates in the trivial light-cone vacuum emerge if defined as short-time limits of fermion propagators. In gauge theories, the necessary inclusion of a gauge string in combination with the characteristic light-cone infrared singularities contain the relevant non-perturbative ingredients responsible for formation of the condensate, as demonstrated for the 't Hooft model.Comment: 4 pages, Revtex

Two Langevin equations in the Doi-Peliti formalism

A system-size expansion method is incorporated into the Doi-Peliti formalism for stochastic chemical kinetics. The basic idea of the incorporation is to introduce a new decomposition of unity associated with a so-called Cole-Hopf transformation. This approach elucidates a relationship between two different Langevin equations; one is associated with a coherent-state path-integral expression and the other describes density fluctuations. A simple reaction scheme $X \rightleftarrows X+X$ is investigated as an illustrative example.Comment: 14page

Dephasing of coupled spin qubit system during gate operations due to background charge fluctuations

It has been proposed that a quantum computer can be constructed based on electron spins in quantum dots or based on a superconducting nanocircuit. During two-qubit operations, the fluctuation of the coupling parameters is a critical factor. One source of such fluctuation is the stirring of the background charges. We focused on the influence of this fluctuation on a coupled spin qubit system. The induced fluctuation in exchange coupling changes the amount of entanglement, fidelity, and purity. In our previous study, the background charge fluctuations were found to be an important channel of dephasing for a single Josephson qubit.Comment: 10 pages, 7 figure. to be publishe

Monte Carlo Renormalization Group Analysis of Lattice ϕ4\phi^4 Model in D=3,4D=3,4

We present a simple, sophisticated method to capture renormalization group flow in Monte Carlo simulation, which provides important information of critical phenomena. We applied the method to $D=3,4$ lattice $\phi^4$ model and obtained renormalization flow diagram which well reproduces theoretically predicted behavior of continuum $\phi^4$ model. We also show that the method can be easily applied to much more complicated models, such as frustrated spin models.Comment: 13 pages, revtex, 7 figures. v1:Submitted to PRE. v2:considerably reduced redundancy of presentation. v3:final version to appear in Phys.Rev.

Monte Carlo renormalization group study of the Heisenberg and XY antiferromagnet on the stacked triangular lattice and the chiral ϕ4\phi^4 model

With the help of the improved Monte Carlo renormalization-group scheme, we numerically investigate the renormalization group flow of the antiferromagnetic Heisenberg and XY spin model on the stacked triangular lattice (STA-model) and its effective Hamiltonian, 2N-component chiral $\phi^4$ model which is used in the field-theoretical studies. We find that the XY-STA model with the lattice size $126\times 144 \times 126$ exhibits clear first-order behavior. We also find that the renormalization-group flow of STA model is well reproduced by the chiral $\phi^4$ model, and that there are no chiral fixed point of renormalization-group flow for N=2 and 3 cases. This result indicates that the Heisenberg-STA model also undergoes first-order transition.Comment: v1:15 pages, 15 figures v2:updated references v3:added comments on the higher order irrelevant scaling variables v4:added results of larger sizes v5:final version to appear in J.Phys.Soc.Jpn Vol.72, No.

Proteins to Order Use of Synthetic DNA to Generate Site-Specific Mutations

The ability to cause specific changes in the amino acid sequences of proteins would greatly advance studies on the influence of protein structure on biochemical function. If the desired changes can once be made in the nucleic acid which encodes the protein, one can use cloning in an appropriate microorganism to produce essentially limitless quantities of the mutant protein. We describe here the application of oligonucleotide-directed site-specific mutagenesis to accomplish this objective for the enzyme B-lactamase, the gene for which is contained in the plasmid pBR322. The method uses a procedure to screen for mutant clones which depends on the DNA in the various colonies and not on the properties of the mutant protein; the method can, therefore, be widely applied and does not require, in each separate case, the development of a screening procedure which depends on some phenotypic difference between mutant and wild-type protein

Advantages of acute brain slices prepared at physiological temperature in the characterization of synaptic functions

Acute brain slice preparation is a powerful experimental model for investigating the characteristics of synaptic function in the brain. Although brain tissue is usually cut at ice-cold temperature (CT) to facilitate slicing and avoid neuronal damage, exposure to CT causes molecular and architectural changes of synapses. To address these issues, we investigated ultrastructural and electrophysiological features of synapses in mouse acute cerebellar slices prepared at ice-cold and physiological temperature (PT). In the slices prepared at CT, we found significant spine loss and reconstruction, synaptic vesicle rearrangement and decrease in synaptic proteins, all of which were not detected in slices prepared at PT. Consistent with these structural findings, slices prepared at PT showed higher release probability. Furthermore, preparation at PT allows electrophysiological recording immediately after slicing resulting in higher detectability of long-term depression (LTD) after motor learning compared with that at CT. These results indicate substantial advantages of the slice preparation at PT for investigating synaptic functions in different physiological conditions

Individual charge traps in silicon nanowires: Measurements of location, spin and occupation number by Coulomb blockade spectroscopy

We study anomalies in the Coulomb blockade spectrum of a quantum dot formed in a silicon nanowire. These anomalies are attributed to electrostatic interaction with charge traps in the device. A simple model reproduces these anomalies accurately and we show how the capacitance matrices of the traps can be obtained from the shape of the anomalies. From these capacitance matrices we deduce that the traps are located near or inside the wire. Based on the occurrence of the anomalies in wires with different doping levels we infer that most of the traps are arsenic dopant states. In some cases the anomalies are accompanied by a random telegraph signal which allows time resolved monitoring of the occupation of the trap. The spin of the trap states is determined via the Zeeman shift.Comment: 9 pages, 8 figures, v2: section on RTS measurements added, many improvement