5,450 research outputs found
Steady States of Infinite-Size Dissipative Quantum Chains via Imaginary Time Evolution
Directly in the thermodynamic limit, we show how to combine imaginary and
real time evolution of tensor networks to efficiently and accurately find the
nonequilibrium steady states (NESS) of one-dimensional dissipative quantum
lattices governed by the Lindblad master equation. The imaginary time evolution
first bypasses any highly correlated portions of the real-time evolution
trajectory by directly converging to the weakly correlated subspace of the
NESS, after which real time evolution completes the convergence to the NESS
with high accuracy. We demonstrate the power of the method with the dissipative
transverse field quantum Ising chain. We show that a crossover of an order
parameter shown to be smooth in previous finite-size studies remains smooth in
the thermodynamic limit.Comment: 5+3 pages, 5 figures, 2 table
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
Smart-Pixel Cellular Neural Networks in Analog Current-Mode CMOS Technology
This paper presents a systematic approach to design CMOS chips with concurrent picture acquisition and processing capabilities. These chips consist of regular arrangements of elementary units, called smart pixels. Light detection is made with vertical CMOS-BJT’s connected in a Darlington structure. Pixel smartness is achieved by exploiting the Cellular Neural Network paradigm [1], [2], incorporating at each pixel location an analog computing cell which interacts with those of nearby pixels. We propose a current-mode implementation technique and give measurements from two 16 x 16 prototypes in a single-poly double-metal CMOS n-well 1.6-µm technology. In addition to the sensory and processing circuitry, both chips incorporate light-adaptation circuitry for automatic contrast adjustment. They obtain smart-pixel densities up to 89 units/mm2, with a power consumption down to 105 µW/unit and image processing times below 2 µs
Boolean Dynamics with Random Couplings
This paper reviews a class of generic dissipative dynamical systems called
N-K models. In these models, the dynamics of N elements, defined as Boolean
variables, develop step by step, clocked by a discrete time variable. Each of
the N Boolean elements at a given time is given a value which depends upon K
elements in the previous time step.
We review the work of many authors on the behavior of the models, looking
particularly at the structure and lengths of their cycles, the sizes of their
basins of attraction, and the flow of information through the systems. In the
limit of infinite N, there is a phase transition between a chaotic and an
ordered phase, with a critical phase in between.
We argue that the behavior of this system depends significantly on the
topology of the network connections. If the elements are placed upon a lattice
with dimension d, the system shows correlations related to the standard
percolation or directed percolation phase transition on such a lattice. On the
other hand, a very different behavior is seen in the Kauffman net in which all
spins are equally likely to be coupled to a given spin. In this situation,
coupling loops are mostly suppressed, and the behavior of the system is much
more like that of a mean field theory.
We also describe possible applications of the models to, for example, genetic
networks, cell differentiation, evolution, democracy in social systems and
neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical
Sciences Serie
Phase diagram of incoherently driven strongly correlated photonic lattices
We explore theoretically the nonequilibrium photonic phases of an array of
coupled cavities in presence of incoherent driving and dissipation. In
particular, we consider a Hubbard model system where each site is a Kerr
nonlinear resonator coupled to a two-level emitter, which is pumped
incoherently. Within a Gutzwiller mean-field approach, we determine the
steady-state phase diagram of such a system. We find that, at a critical value
of the inter-cavity photon hopping rate, a second-order nonequilibrium phase
transition associated with the spontaneous breaking of the symmetry
occurs. The transition from an incompressible Mott-like photon fluid to a
coherent delocalized phase is driven by commensurability effects and not by the
competition between photon hopping and optical nonlinearity. The essence of the
mean-field predictions is corroborated by finite-size simulations obtained with
matrix product operators and corner-space renormalization methods.Comment: 12 pages, 9 figure
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