First order dipolar phase transition in the Dicke model with infinitely coordinated frustrating interaction

We found analytically a first order quantum phase transition in the Cooper pair box array of $N$ low-capacitance Josephson junctions capacitively coupled to a resonant photon in a microwave cavity. The Hamiltonian of the system maps on the extended Dicke Hamiltonian of $N$ spins one-half with infinitely coordinated antiferromagnetic (frustrating) interaction. This interaction arises from the gauge-invariant coupling of the Josephson junctions phases to the vector potential of the resonant photon field. In $N \gg 1$ semiclassical limit, we found a critical coupling at which ground state of the system switches to the one with a net collective electric dipole moment of the Cooper pair boxes coupled to superradiant equilibrium photonic condensate. This phase transition changes from the first to second order if the frustrating interaction is switched off. A self-consistently `rotating' Holstein-Primakoff representation for the Cartesian components of the total superspin is proposed, that enables to trace both the first and the second order quantum phase transitions in the extended and standard Dicke models respectively.Comment: 12 pages, 10 figure

Isolated zeros in the spectral function as signature of a quantum continuum

We study the observable properties of quantum systems which involve a quantum continuum as a subpart. We show in a very general way that in any system, which consists of at least two isolated states coupled to a continuum, the spectral function of one of the states exhibits an isolated zero at the energy of the other state. Several examples of quantum systems exhibiting such isolated zeros are discussed. Although very general, this phenomenon can be particularly useful as an indirect detection tool for the continuum spectrum in the lab realizations of quantum critical behavior.Comment: 10 pages, 6 figures; Published versio

Solvable model for a charge-4e4e superconductor

A charge-$4e$ superconductor forms due to the condensation of quartets of electrons. While in previous works the mechanism for the formation of charge-$4e$ superconductivity has been analyzed in terms of the binding of Cooper pairs in unconventional superconductors, its properties in the fermionic sector have not been studied systematically due to its inherently interacting nature even at the mean-field level. Here we propose a solvable model for a charge-$4e$ superconductor -- a spinful version of the Sachdev-Ye-Kitaev model with an anomalous quartic term. We show that the ground state is gapless and resembles a heavy Fermi liquid. We analytically solve for the superfluid density and show that it is perturbative in the strength of the charge-$4e$ order parameter, in sharp contrast with a regular (charge-$2e$) superconductor. Upon lowering temperature, we show that the correlation between charge-$4e$ order and regular interaction terms can drive a first-order phase transition to a charge-$2e$ superconducting state.Comment: 24 pages, 3 figure

Area-Efficient FPGA Implementation of Minimalistic Convolutional Neural Network Using Residue Number System

Convolutional Neural Networks (CNN) is the promising tool for solving task of image recognition in computer vision systems. However, the most known implementation of CNNs require a significant amount of memory for storing weights in training and work. To reduce the resource costs of CNN implementation we propose the architecture that separated on hardware and software parts for performance optimization. Also we propose to use Residue Number System (RNS) arithmetic in the hardware part which implements the convolutional layer of CNN. Software simulation using Matlab 2017b shows that CNN with a minimum number of layers can be quickly and successfully trained. Hardware simulation using FPGA Kintex7 xc7k70tfbg484-2 demonstrates that using RNS in convolutional layer of CNN allows to reduce hardware costs by 32% compared with the traditional approach based on the binary number system