In a recent work, Bindini and De Pascale have introduced a regularization of N-particle symmetric probabilities that preserves their one-particle marginals. In this short note, we extend their ...construction to mixed quantum fermionic states. This enables us to prove the convergence of the Levy–Lieb functional in Density Functional Theory, to the corresponding multi-marginal optimal transport in the semi-classical limit. Our result holds for mixed states of any particle number N, with or without spin.
Dans un travail récent, Bindini et de Pascale ont introduit une régularisation des probabilités symétriques décrivant N particules indiscernables, qui préserve la densité à une particule. Nous étendons ici leur construction aux états quantiques mixtes de fermions. Ceci nous permet de démontrer la convergence de la fonctionnelle de Levy–Lieb, objet central de la théorie de la fonctionnelle de densité (DFT), vers le transport optimal multi-marges associé, à la limite semi-classique. Notre résultat est valable pour les états mixtes de n'importe quel nombre de particules N, avec ou sans spin.
Preparing quantum thermal states on a quantum computer is in general a difficult task. We provide a procedure to prepare a thermal state on a quantum computer with a logarithmic depth circuit of ...local quantum channels assuming that the thermal state correlations satisfy the following two properties: (i) the correlations between two regions are exponentially decaying in the distance between the regions, and (ii) the thermal state is an approximate Markov state for shielded regions. We require both properties to hold for the thermal state of the Hamiltonian on any induced subgraph of the original lattice. Assumption (ii) is satisfied for all commuting Gibbs states, while assumption (i) is satisfied for every model above a critical temperature. Both assumptions are satisfied in one spatial dimension. Moreover, both assumptions are expected to hold above the thermal phase transition for models without any topological order at finite temperature. As a building block, we show that exponential decay of correlation (for thermal states of Hamiltonians on all induced subgraphs) is sufficient to efficiently estimate the expectation value of a local observable. Our proof uses quantum belief propagation, a recent strengthening of strong sub-additivity, and naturally breaks down for states with topological order.
The well-known 5-parameter isometry group of plane gravitational waves in 4 dimensions is identified as Lévy-Leblond's Carroll group in 2+1 dimensions with no rotations. Our clue is that plane waves ...are Bargmann spaces into which Carroll manifolds can be embedded. We also comment on the scattering of light by a gravitational wave and calculate its electric permittivity considered as an impedance-matched metamaterial.
Having a distance measure between quantum states satisfying the right properties is of fundamental importance in all areas of quantum information. In this work, we present a systematic study of the
...geometric Rényi divergence
(GRD), also known as the maximal Rényi divergence, from the point of view of quantum information theory. We show that this divergence, together with its extension to channels, has many appealing structural properties, which are not satisfied by other quantum Rényi divergences. For example we prove a chain rule inequality that immediately implies the “amortization collapse” for the geometric Rényi divergence, addressing an open question by Berta et al. Letters in Mathematical Physics 110:2277–2336, 2020, Equation (55) in the area of quantum channel discrimination. As applications, we explore various channel capacity problems and construct new channel information measures based on the geometric Rényi divergence, sharpening the previously best-known bounds based on the max-relative entropy while still keeping the new bounds single-letter and efficiently computable. A plethora of examples are investigated and the improvements are evident for almost all cases.
We present a theory of periodically driven, many-body localized (MBL) systems. We argue that MBL persists under periodic driving at high enough driving frequency: The Floquet operator (evolution ...operator over one driving period) can be represented as an exponential of an effective time-independent Hamiltonian, which is a sum of quasi-local terms and is itself fully MBL. We derive this result by constructing a sequence of canonical transformations to remove the time-dependence from the original Hamiltonian. When the driving evolves smoothly in time, the theory can be sharpened by estimating the probability of adiabatic Landau–Zener transitions at many-body level crossings. In all cases, we argue that there is delocalization at sufficiently low frequency. We propose a phase diagram of driven MBL systems.
O(N) Random Tensor Models Carrozza, Sylvain; Tanasa, Adrian
Letters in mathematical physics,
11/2016, Letnik:
106, Številka:
11
Journal Article
Recenzirano
Odprti dostop
We define in this paper a class of three-index tensor models, endowed with
O
(
N
)
⊗
3
invariance (
N
being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, ...a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the
U
(
N
) invariant models. We first exhibit the existence of a large
N
expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large
N
expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.
Inspired by recent work by Closset, Kim, and Willett, we derive a new formula for the superconformal (or supersymmetric) index of 4D
N
=
1
theories. Such a formula is a finite sum, over the solution ...set of certain transcendental equations that we dub Bethe Ansatz Equations, of a function evaluated at those solutions.
The segregation of solutes at dislocations in a polycrystalline and a single crystal nickel-based superalloy is studied. Our observations confirm the often assumed but yet unproven diffusion along ...dislocations via pipe diffusion. Direct observation and quantitative, near-atomic scale segregation of chromium and cobalt at dislocations within γ' precipitates and at interfacial dislocations leading to the partial or complete dissolution of γ' precipitates at elevated temperatures is presented. Our results allow us to elucidate the physical mechanism by which pipe diffusion initiates the undesirable dissolution of γ' precipitates.
Display omitted
We present a rigorous derivation of the point vortex model starting from the two-dimensional nonlinear Schrödinger equation, from the Hamiltonian perspective, in the limit of well-separated, subsonic ...vortices on the background of a spatially infinite strong condensate. As a corollary, we calculate to high accuracy the self-energy of an isolated elementary Pitaevskii vortex.
PDF
