Stability of velocity-Verlet- and Liouville-operator-derived algorithms to integrate non-Hamiltonian systems

We investigate the difference between the velocity Verlet and the Liouville-operator-derived (LOD) algorithms by studying two non-Hamiltonian systems, one dissipative and the other conservative, for which the Jacobian of the transformation can be determined exactly. For the two systems, we demonstrate that (1) the velocity Verlet scheme fails to integrate the former system while the first- and second-order LOD schemes succeed, (2) some first-order LOD fails to integrate the latter system while the velocity Verlet and the other first- and second-order schemes succeed. We have shown that the LOD schemes are stable for the former system by determining the explicit forms of the shadow Hamiltonians which are exactly conserved by the schemes. We have shown that Jacobian of the velocity Verlet scheme for the former system and that of the first-order LOD scheme for the latter system are always smaller than the exact values, and therefore, the schemes are unstable. The decomposition-order dependence of LOD schemes is also considered.Comment: 11 pages, 8 figures. New results are adde

Non-equilibrium Relaxation Analysis on Two-dimensional Melting

The melting transition in the hard-disk system is considered. Non-equilibrium relaxation analysis of the six-fold bond-orientational order parameter has been carried out. The critical point between the hexatic and the fluid phase is determined on the basis of the dynamic scaling hypothesis. The value of the critical exponent $\eta$ is determined from the fluctuation of the order parameter at the criticality as $\eta = 0.25(2)$ which is consistent with the prediction by the Kosterlitz-Thouless-Halperin-Nelson-Young theory.Comment: 8 pages, 5 figures. submitted to Prog. Theor. Phys. Suppl. as a proceedings of Symposium on the 50th anniversary of the Alder transitio

Mathematical Derivation of Chiral Anomaly in Lattice Gauge Theory with Wilson's Action

Chiral U(1) anomaly is derived with mathematical rigor for a Euclidean fermion coupled to a smooth external U(1) gauge field on an even dimensional torus as a continuum limit of lattice regularized fermion field theory with the Wilson term in the action. The present work rigorously proves for the first time that the Wilson term correctly reproduces the chiral anomaly.Comment: 33 pages, LaTe

Triviality of hierarchical O(N) spin model in four dimensions with large N

The renormalization group transformation for the hierarchical O(N) spin model in four dimensions is studied by means of characteristic functions of single-site measures, and convergence of the critical trajectory to the Gaussian fixed point is shown for a sufficiently large N. In the strong coupling regime, the trajectory is controlled by the help of the exactly solved O(\infty) trajectory, while, in the weak coupling regime, convergence to the Gaussian fixed point is shown by power decay of the effective coupling constant.Comment: AMSLaTe

Charge-density wave induced by combined electron-electron and electron-phonon interactions in 1TT-TiSe2_2: A variational Monte Carlo study

To clarify the origin of a charge-density wave (CDW) phase in 1$T$-TiSe$_2$, we study the ground state property of a half-filled two-band Hubbard model in a triangular lattice including electron-phonon interaction. By using the variational Monte Carlo method, the electronic and lattice degrees of freedom are both treated quantum mechanically on an equal footing beyond the mean-field approximation. We find that the cooperation between Coulomb interaction and electron-phonon interaction is essential to induce the CDW phase. We show that the "pure" exciton condensation without lattice distortion is difficult to realize under the poor nesting condition of the underlying Fermi surface. Furthermore, by systematically calculating the momentum resolved hybridization between the two bands, we examine the character of electron-hole pairing from the viewpoint of BCS-BEC crossover within the CDW phase and find that the strong-coupling BEC-like pairing dominates. We therefore propose that the CDW phase observed in 1$T$-TiSe$_2$ originates from a BEC-like electron-hole pairing.Comment: 7 pages, 4 figure

Single-Flux-Quantum Bipolar Digital-to-Analog Converter Comprising Polarity-Switchable Double-Flux-Quantum Amplifier

We present a single-flux-quantum (SFQ)-based digital-to-analog converter (DAC) generating bipolar output voltages, in which the key component is a polarity-switchable double-flux-quantum amplifier (PS-DFQA). The DAC comprised a dc/SFQ converter, an 8-bit variable pulse-number-multiplier (PNM), and a 8-fold PS-DFQA integrated on a single chip. SFQ pulse-frequency modulation was employed to realize variable output voltage amplitude, for which the multiplication factor of the variable-PNM was controlled by a commercial data generator situated at room temperature. The variable-PNM realized 8-bit resolution with a multiplication factor between 0 and 255. Bias currents fed to the 8-fold PS-DFQA were polarity-switched in synchronization with the digital code for the variable-PNM. The whole circuits including I/O elements were designed using SFQ cell libraries, and fabricated using a niobium integration process. Sinusoidal bipolar voltage waveform of 0.38 mVpp was demonstrated using a reference signal source of 43.94 MHz