Optimal Frobenius light cone in spin chains with power-law interactions

In non-relativistic quantum theories the Lieb-Robinson bound defines an effective light cone with exponentially small tails outside of it. In this work we use it to derive a bound for the correlation function of two local disjoint observables at different times if the initial state has a power-law decay. We show that the exponent of the power-law of the bound is identical to the initial (equilibrium) decay. We explicitly verify this result by studying the full dynamics of the susceptibilities and correlations in the exactly solvable Luttinger model after a sudden quench from the non-interacting to the interacting model.

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NEW SCALING VARIABLE FROM LIGHT-CONE PERTURBATION THEORY

International Journal of Modern Physics A ◽

10.1142/s0217751x91000216 ◽

1991 ◽

Vol 06 (03) ◽

pp. 345-363 ◽

Cited By ~ 12

Author(s):

BO-QIANG MA ◽

JI SUN

Keyword(s):

Perturbation Theory ◽

Power Law ◽

Light Cone ◽

Operator Product Expansion ◽

Free Field ◽

Field Operator ◽

Order Effect ◽

Operator Product ◽

Bjorken Scaling ◽

Twist Effect

We argue from both the quark language and the free field light-cone expansion in light-cone perturbation theory that the constraint of overall “energy” conservation in deep inelastic lepton-nucleon scattering yields a similar new scaling variable xp, which reduces to the Weizmann variable, the Bloom-Gilman variable and the Bjorken variable at some approximations. The xp rescaling is expected to be a good scaling variable, and hence gives strong power-law type corrections to the deviations of Bjorken scaling. An understanding of this xp rescaling from both the free field operator product expansion (OPE) and the ordinary OPE is also given, indicating it is likely a higher order effect in the coefficient functions, i.e. it does not belong to the higher twist effect. Therefore this xp rescaling is likely a new effect contributing to the power-law type corrections.

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Dependence on the environment of the abundance function of light-cone simulation dark matter haloes

Astronomy and Astrophysics ◽

10.1051/0004-6361/201731440 ◽

2018 ◽

Vol 616 ◽

pp. A137 ◽

Cited By ~ 2

Author(s):

Maria Chira ◽

Manolis Plionis ◽

Pier-Stefano Corasaniti

Keyword(s):

Dark Matter ◽

Power Law ◽

Phenomenological Model ◽

Light Cone ◽

Dark Matter Halo ◽

Nearest Neighbour ◽

Spherical Region ◽

Theoretical Mass ◽

Mass Functions ◽

Characteristic Mass

Aims. We study the dependence of the halo abundance function (AF) on different environments in a whole-sky ΛCDM light-cone halo catalogue extending to z ~ 0.65, using a simple and well-defined halo isolation criterion. Methods. The isolation status of each individual dark matter halo is determined by the distance to its nearest neighbour, which defines the maximum spherical region devoid of halos above a threshold mass around it (although the true size of such region may be much larger since it is not necessarily spherical). A versatile double power-law Schechter function is used to fit the dark matter halo AF, and its derived parameters are studied as a function of halo isolation status. Results. (a) Our function fits the halo abundances for all halo isolation statuses extremely well, while the well-established theoretical mass functions, integrated over the volume of the light-cone, provide an adequate but poorer fit than our phenomenological model. (b) As expected, and in agreement with other studies based on snap-shot simulations, we find significant differences of the halo abundance function as a function of halo isolation, indicating different rates of halo formation. The slope of the power law and the characteristic mass of the Schechter-like fitting function decrease with isolation, a result consistent with the formation of less massive haloes in lower density regions. (c) We find an unexpected upturn of the characteristic mass of the most isolated haloes of our sample. This upturn originates and characterises only the higher redshift regime (z ≳ 0.45), which probably implies a significant and recent evolution of the isolation status of the most isolated and most massive haloes.

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The thermal SZ power spectrum

Proceedings of the International Astronomical Union ◽

10.1017/s1743921316004415 ◽

2015 ◽

Vol 11 (A29B) ◽

pp. 59-59

Author(s):

Klaus Dolag ◽

Eiichiro Komatsu ◽

Rashid Sunyaev

Keyword(s):

Probability Distribution ◽

Power Spectrum ◽

Chemical Evolution ◽

Power Law ◽

Light Cone ◽

High Redshift ◽

Cosmological Parameters ◽

Dynamical Simulation ◽

Virial Mass ◽

The One

AbstractThe Magneticum Pathfinder (www.magneticum.org) cosmological, hydro-dynamical simulation (896h-1Mpc)3 follows in detail the thermal and chemical evolution of the ICM as well as the evolution of SMBHs and their associated feedback processes. We demonstrate that assuming cosmological parameters inferred from the CMB, the thermal SZ power spectrum as observed by PLANCK is well matched by the deep light-cones constructed from these cosmological simulations. The thermal SZ prediction from the full SZ maps are significantly exceeding previous templates at large l (e.g., l > 1000) and therefore predict a significantly larger contribution to the signal at l = 3000 compared to previous findings. The excess of positive values within the probability distribution of the thermal SZ signal within the simulated light-cone agrees with the one seen by PLANCK. This excess signal follows a power law shape with an index of roughly -3.2. The bulk of the thermal SZ signal originates from clusters and groups which form between z = 0 and z ≈ 2 where at high redshift (z > 1) significant part of the signal originates from proto-cluster regions, which are not yet virialized. The simulation predicts a mean fluctuating Compton Y value of 1.18 × 10-6, with a remaining contribution of almost 5 ×10-7 when removing contribution from halos above a virial mass of 1013 M⊙/h.

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Quantum dynamics of disordered spin chains with power-law interactions

Physical Review A ◽

10.1103/physreva.99.033610 ◽

2019 ◽

Vol 99 (3) ◽

Cited By ~ 15

Author(s):

A. Safavi-Naini ◽

M. L. Wall ◽

O. L. Acevedo ◽

A. M. Rey ◽

R. M. Nandkishore

Keyword(s):

Power Law ◽

Quantum Dynamics ◽

Spin Chains

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“Light-Cone” Dynamics After Quantum Quenches in Spin Chains

Physical Review Letters ◽

10.1103/physrevlett.113.187203 ◽

2014 ◽

Vol 113 (18) ◽

Cited By ~ 119

Author(s):

Lars Bonnes ◽

Fabian H. L. Essler ◽

Andreas M. Läuchli

Keyword(s):

Light Cone ◽

Spin Chains ◽

Quantum Quenches

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Breaking of Huygens-Fresnel principle in inhomogeneous Tomonaga-Luttinger liquids

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8121/ac39cc ◽

2021 ◽

Author(s):

Marek Gluza ◽

Per Moosavi ◽

Spyros Sotiriadis

Keyword(s):

Light Cone ◽

Ultracold Atoms ◽

Spin Chains ◽

Many Body ◽

Luttinger Liquids ◽

Main Motivation ◽

One Dimensional ◽

Superconducting Circuits ◽

Many Body Systems ◽

Two Parameters

Abstract Tomonaga-Luttinger liquids (TLLs) can be used to eﬀectively describe one-dimensional quantum many-body systems such as ultracold atoms, charges in nanowires, superconducting circuits, and gapless spin chains. Their properties are given by two parameters, the propagation velocity and the Luttinger parameter. Here we study inhomogeneous TLLs where these are promoted to functions of position and demonstrate that they profoundly aﬀect the dynamics: In general, besides curving the light cone, we show that propagation is no longer ballistically localized to the light-cone trajectories, diﬀerent from standard homogeneous TLLs. Speciﬁcally, if the Luttinger parameter depends on position, the dynamics features pronounced spreading into the light cone, which cannot be understood via a simple superposition of waves as in the Huygens-Fresnel principle. This is the case for ultracold atoms in a parabolic trap, which serves as our main motivation, and we discuss possible experimental observations in such systems.

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