160 research outputs found
Emergent Irreversibility And Entanglement Spectrum Statistics
No full textWe study the problem of irreversibility when the dynamical evolution of a many-body system is described by a stochastic quantum circuit. Such evolution is more general than a Hamiltonian one, and since energy levels are not well defined, the well-established connection between the statistical fluctuations of the energy spectrum and irreversibility cannot be made. We show that the entanglement spectrum provides a more general connection. Irreversibility is marked by a failure of a disentangling algorithm and is preceded by the appearance of Wigner-Dyson statistical fluctuations in the entanglement spectrum. This analysis can be done at the wave-function level and offers an alternative route to study quantum chaos and quantum integrability. © 2014 American Physical Society
Facultative Mixity in the Area of Freedom Security and Justice
No full textThis contribution investigates the extent to which facultative mixity as a dimension of EU external relation exists in the Area of Freedom Security and Justice. The analysis addresses two questions. Firstly, what role may facultative mixity play, in principle, in the afsj? And secondly, to what extent, and in which context, has the Council made use of facultative mixity in the afsj, in practice? The first part of the paper addresses the first question, by discussing the role of facultative mixity in the externalisation of the afsj (section 2). The second part responds to the second question, by analysing the existing practice concerning mixed agree- ments, focusing on the Council’s authorisation to sign international agree- ments related to the afsj (section 3)
Long tunneling contact as a probe of fractional quantum Hall neutral edge modes
No full textWe study the tunneling current between edge states of quantum Hall liquids across a single long-contact region and predict a resonance at a bias voltage set by the scale of the edge velocity. For typical devices and edge velocities associated with charged modes, this resonance occurs outside the physically accessible bias domain. However, for edge states that are expected to support neutral modes, such as the ν=2/3 and ν=5/2 Pfaffian and anti-Pfaffian states, the neutral velocity can be orders of magnitude smaller than the charged mode and if so the resonance would be accessible. Therefore, such long tunneling contacts can resolve the presence of neutral edge modes in certain quantum Hall liquids.United States. Dept. of Energy (Grant No. DE-FG02-06ER46316
Irreversibility And Entanglement Spectrum Statistics In Quantum Circuits
No full textWe show that in a quantum system evolving unitarily under a stochastic quantum circuit the notions of irreversibility, universality of computation, and entanglement are closely related. As the state evolves from an initial product state, it gets asymptotically maximally entangled. We define irreversibility as the failure of searching for a disentangling circuit using a Metropolis-like algorithm. We show that irreversibility corresponds to Wigner-Dyson statistics in the level spacing of the entanglement eigenvalues, and that this is obtained from a quantum circuit made from a set of universal gates for quantum computation. If, on the other hand, the system is evolved with a non-universal set of gates, the statistics of the entanglement level spacing deviates from Wigner-Dyson and the disentangling algorithm succeeds. These results open a new way to characterize irreversibility in quantum systems
Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics
No full textClifford circuits are insufficient for universal quantum computation or creating t-designs with t ≥ 4. While the entanglement entropy is not a telltale of this insufficiency, the entanglement spectrum of a time evolved random product state is: the entanglement levels are Poisson-distributed for circuits restricted to the Clifford gate-set, while the levels follow Wigner-Dyson statistics when universal gates are used. In this paper we show, using finite-size scaling analysis of different measures of level spacing statistics, that in the thermodynamic limit, inserting a single T (π/8) gate in the middle of a random Clifford circuit is sufficient to alter the entanglement spectrum from a Poisson to a Wigner-Dyson distribution
Fluctuations of two-time quantities and time-reparametrization invariance in spin-glasses
No full textThis article is a contribution to the understanding of fluctuations in the out of equilibrium dynamics of glassy systems. By extending theoretical ideas based on the assumption that time-reparametrization invariance develops asymptotically we deduce the scaling properties of diverse high-order correlation functions. We examine these predictions with numerical tests in a standard glassy model, the 3d Edwards-Anderson spin-glass, and in a system where time-reparametrization invariance is not expected to hold, the 2d ferromagnetic Ising model, both at low temperatures. Our results enlighten a qualitative difference between the fluctuation properties of the two models and show that scaling properties conform to the time-reparametrization invariance scenario in the former but not in the latter
Heat Pumping in Nanomechanical Systems
No full textWe propose using a phonon pumping mechanism to transfer heat from a cold to a hot body using a propagating modulation of the medium connecting the two bodies. This phonon pump can cool nanomechanical systems without the need for active feedback. We compute the lowest temperature that this refrigerator can achieve.Fil: Chamon, Claudio. Boston University; Estados UnidosFil: Mucciolo, Eduardo R.. University Of Central Florida; Estados UnidosFil: Arrachea, Liliana del Carmen. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Capaz, Rodrigo B.. Universidade Federal do Rio de Janeiro; Brasi
Entanglement complexity in quantum many-body dynamics, thermalization, and localization
No full textEntanglement is usually quantified by von Neumann entropy, but its properties are much more complex than what can be expressed with a single number. We show that the three distinct dynamical phases known as thermalization, Anderson localization, and many-body localization are marked by different patterns of the spectrum of the reduced density matrix for a state evolved after a quantum quench. While the entanglement spectrum displays Poisson statistics for the case of Anderson localization, it displays universal Wigner-Dyson statistics for both the cases of many-body localization and thermalization, albeit the universal distribution is asymptotically reached within very different time scales in these two cases. We further show that the complexity of entanglement, revealed by the possibility of disentangling the state through a Metropolis-like algorithm, is signaled by whether the entanglement spectrum level spacing is Poisson or Wigner-Dyson distributed
Two-Component Structure in the Entanglement Spectrum of Highly Excited States
No full textWe study the entanglement spectrum of highly excited eigenstates of two known models that exhibit a many-body localization transition, namely the one-dimensional random-field Heisenberg model and the quantum random energy model. Our results indicate that the entanglement spectrum shows a “two-component” structure: a universal part that is associated with random matrix theory, and a nonuniversal part that is model dependent. The nonuniversal part manifests the deviation of the highly excited eigenstate from a true random state even in the thermalized phase where the eigenstate thermalization hypothesis holds. The fraction of the spectrum containing the universal part decreases as one approaches the critical point and vanishes in the localized phase in the thermodynamic limit. We use the universal part fraction to construct an order parameter for measuring the degree of randomness of a generic highly excited state, which is also a promising candidate for studying the many-body localization transition. Two toy models based on Rokhsar-Kivelson type wave functions are constructed and their entanglement spectra are shown to exhibit the same structure
Quantizing Majorana fermions in a superconductor
No full textA Dirac-type matrix equation governs surface excitations in a topological insulator in contact with an s-wave superconductor. The order parameter can be homogenous or vortex valued. In the homogenous case a winding number can be defined whose nonvanishing value signals topological effects. A vortex leads to a static, isolated, zero-energy solution. Its mode function is real and has been called “Majorana.” Here we demonstrate that the reality/Majorana feature is not confined to the zero-energy mode but characterizes the full quantum field. In a four-component description a change in basis for the relevant matrices renders the Hamiltonian imaginary and the full, space-time-dependent field is real, as is the case for the relativistic Majorana equation in the Majorana matrix representation. More broadly, we show that the Majorana quantization procedure is generic to superconductors, with or without the Dirac structure, and follows from the constraints of fermionic statistics on the symmetries of Bogoliubov-de Gennes Hamiltonians. The Hamiltonian can always be brought to an imaginary form, leading to equations of motion that are real with quantized real-field solutions. Also we examine the Fock space realization of the zero-mode algebra for the Dirac-type systems. We show that a two-dimensional representation is natural, in which fermion parity is preserved.United States. Dept. of Energy (DEF-06ER46316)United States. Dept. of Energy (91ER40676)United States. Dept. of Energy (05ER41360
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