Collision of one-dimensional fermion clusters

We study cluster-cluster collisions in one-dimensional Fermi systems with particular emphasis on the non-trivial quantum effects of the collision dynamics. We adopt the Fermi-Hubbard model and the time-dependent density matrix renormalization group method to simulate collision dynamics between two fermion clusters of different spin states with contact interaction. It is elucidated that the quantum effects become extremely strong with the interaction strength, leading to the transmittance much more enhanced than expected from semiclassical approximation. We propose a concise model based on one-to-one collisions, which unveils the origin of the quantum effects and also explains the overall properties of the simulation results clearly. Our concise model can quite widely describe the one-dimensional collision dynamics with contact interaction. Some potential applications, such as repeated collisions, are addressed.Comment: 5 pages, 5 figure

Observation of Conduction Band Satellite of Ni Metal by 3p-3d Resonant Inverse Photoemission Study

Resonant inverse photoemission spectra of Ni metal have been obtained across the Ni 3$p$ absorption edge. The intensity of Ni 3$d$ band just above Fermi edge shows asymmetric Fano-like resonance. Satellite structures are found at about 2.5 and 4.2 eV above Fermi edge, which show resonant enhancement at the absorption edge. The satellite structures are due to a many-body configuration interaction and confirms the existence of 3$d^8$ configuration in the ground state of Ni metal.Comment: 4 pages, 3 figures, submitted to Physical Review Letter

Density-matrix renormalization group study of pairing when electron-electron and electron-phonon interactions coexist: effect of the electronic band structure

Density-matrix renormalization group is used to study the pairing when both of electron-electron and electron-phonon interactions are strong in the Holstein-Hubbard model at half-filling in a region intermediate between the adiabatic (Migdal's) and antiadiabatic limits. We have found: (i) the pairing correlation obtained for a one-dimensional system is nearly degenerate with the CDW correlation in a region where the phonon-induced attraction is comparable with the electron-electron repulsion, but (ii) pairing becomes dominant when we destroy the electron-hole symmetry in a trestle lattice. This provides an instance in which pairing can arise, in a lattice-structure dependent manner, from coexisting electron-electron and electron-phonon interactions.Comment: 4 pages, 3 figures; to appear in Phys. Rev. Let

Computation over galois fields using shiftregisters

This paper presents a technique for readily determining the shiftregister which multiplies by a given element of GF(2m)}, or which raises a given element of GF(2m)} to a given power. A matrix (called a connection matrix) is derived from a primitive polynomial and is corresponded to a particular shiftregister. The nth power of the matrix corresponds to the shiftregister which multiplies by Xn. Examples are presented to illustrate the application of the technique

Time-evolution of the Rule 150 cellular automaton activity from a Fibonacci iteration

The total activity of the single-seeded cellular rule 150 automaton does not follow a one-step iteration like other elementary cellular automata, but can be solved as a two-step vectorial, or string, iteration, which can be viewed as a generalization of Fibonacci iteration generating the time series from a sequence of vectors of increasing length. This allows to compute the total activity time series more efficiently than by simulating the whole spatio-temporal process, or even by using the closed expression.Comment: 4 pages (3 figs included

Onset of Random Matrix Behavior in Scrambling Systems

The fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. A basic scale in such a system is the energy range over which this behavior persists. We define the corresponding time scale by the time at which the linearly growing ramp region in the spectral form factor begins. We call this time $t_{\rm ramp}$. The purpose of this paper is to study this scale in many-body quantum systems that display strong chaos, sometimes called scrambling systems. We focus on randomly coupled qubit systems, both local and $k$-local (all-to-all interactions) and the Sachdev--Ye--Kitaev (SYK) model. Using numerical results for Hamiltonian systems and analytic estimates for random quantum circuits we find the following results. For geometrically local systems with a conservation law we find $t_{\rm ramp}$ is determined by the diffusion time across the system, order $N^2$ for a 1D chain of $N$ qubits. This is analogous to the behavior found for local one-body chaotic systems. For a $k$-local system with conservation law the time is order $\log N$ but with a different prefactor and a different mechanism than the scrambling time. In the absence of any conservation laws, as in a generic random quantum circuit, we find $t_{\rm ramp} \sim \log N$, independent of connectivity.Comment: 61+20 pages, minor errors corrected, and significant edits in Section

Black Holes and Random Matrices

We argue that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems. Our main tool is the Sachdev-Ye-Kitaev (SYK) model, which we use as a simple model of a black hole. We use an analytically continued partition function $|Z(\beta +it)|^2$ as well as correlation functions as diagnostics. Using numerical techniques we establish random matrix behavior at late times. We determine the early time behavior exactly in a double scaling limit, giving us a plausible estimate for the crossover time to random matrix behavior. We use these ideas to formulate a conjecture about general large AdS black holes, like those dual to 4D super-Yang-Mills theory, giving a provisional estimate of the crossover time. We make some preliminary comments about challenges to understanding the late time dynamics from a bulk point of view.Comment: 73 pages, 15 figures, minor errors correcte