We investigate the nonequilibrium dynamics of competing coexisting superconducting (SC) and charge-density wave (CDW) orders in an attractive Hubbard model. A time-periodic laser field Aover →(t) ...lifts the SC-CDW degeneracy, since the CDW couples linearly to the field (Aover →), whereas SC couples in second order (Aover →^{2}) due to gauge invariance. This leads to a striking resonance: When the photon energy is red detuned compared to the equilibrium single-particle energy gap, CDW is enhanced and SC is suppressed, while this behavior is reversed for blue detuning. Both orders oscillate with an emergent slow frequency, which is controlled by the small amplitude of a third induced order, namely η pairing, given by the commutator of the two primary orders. The induced η pairing is shown to control the enhancement and suppression of the dominant orders. Finally, we demonstrate that light-induced superconductivity is possible starting from a predominantly CDW initial state.
In this paper we consider bilinear sparse forms intimately related to iterated commutators of a rather general class of operators. We establish Bloom weighted estimates for these forms in the full ...range of exponents, both in the diagonal and off-diagonal cases. As an application, we obtain new Bloom bounds for commutators of (maximal) rough homogeneous singular integrals and the Bochner–Riesz operator at the critical index. We also raise the question about the sharpness of our estimates. In particular we obtain the surprising fact that even in the case of Calderón–Zygmund operators, the previously known quantitative Bloom bounds are not sharp for the second and higher order commutators.
A
bstract
Heisenberg time evolution under a chaotic many-body Hamiltonian
H
transforms an initially simple operator into an increasingly complex one, as it spreads over Hilbert space. Krylov ...complexity, or ‘K-complexity’, quantifies this growth with respect to a special basis, generated by
H
by successive nested commutators with the operator. In this work we study the evolution of K-complexity in finite-entropy systems for time scales greater than the scrambling time
t
s
>
log(
S
). We prove rigorous bounds on K-complexity as well as the associated Lanczos sequence and, using refined parallelized algorithms, we undertake a detailed numerical study of these quantities in the SYK
4
model, which is maximally chaotic, and compare the results with the SYK
2
model, which is integrable. While the former saturates the bound, the latter stays exponentially below it. We discuss to what extent this is a generic feature distinguishing between chaotic vs. integrable systems.
For two n×n complex matrices A and B, we define the q-deformed commutator as A,Bq:=AB−qBA for a real parameter q. In this paper, we investigate a generalization of the Böttcher-Wenzel inequality ...which gives the sharp upper bound of the (Frobenius) norm of the commutator. In our generalisation, we investigate sharp upper bounds on the q-deformed commutator. This generalization can be studied in two different scenarios: firstly bounds for general matrices, and secondly for traceless matrices. For both scenarios, partial answers and conjectures are given for positive and negative q. In particular, denoting the Frobenius norm by ||.||F, when A or B is normal, we prove the following inequality to be true and sharp: ||A,Bq||F2≤(1+q2)||A||F2||B||F2 for positive q. Also, we conjecture that the same bound is true for positive q when A or B is traceless. For negative q, we conjecture other sharp upper bounds to be true for the generic scenarios and the scenario when A or B is traceless. All conjectures are supported with numerics and proved for n=2.
We find that the effects of a localized perturbation in a chaotic classical many-body system-the classical Heisenberg chain at infinite temperature-spread ballistically with a finite speed even when ...the local spin dynamics is diffusive. We study two complementary aspects of this butterfly effect: the rapid growth of the perturbation, and its simultaneous ballistic (light-cone) spread, as characterized by the Lyapunov exponents and the butterfly speed, respectively. We connect this to recent studies of the out-of-time-ordered commutators (OTOC), which have been proposed as an indicator of chaos in a quantum system. We provide a straightforward identification of the OTOC with a natural correlator in our system and demonstrate that many of its interesting qualitative features are present in the classical system. Finally, by analyzing the scaling forms, we relate the growth, spread, and propagation of the perturbation with the growth of one-dimensional interfaces described by the Kardar-Parisi-Zhang equation.
In this paper, we give a characterization of mixed \(\lambda\)-central bounded mean oscillation space \(\mathrm{CBMO}^{\vec{q},\lambda}(\mathbb{R}^{n})\) via the boundedness of the commutators of ...\(n\)-dimensional Hardy operator \(\mathcal{H}\) and its dual operator \(\mathcal{H}^{*}\) on mixed Lebesgue space \(L^{\vec{p}}(\mathbb{R}^{n})\). In addition, we also establish the boundedness of commutators \(\mathcal{H}_{b}\) and \(\mathcal{H}^{*}_{b}\) generated with \(\mathrm{CBMO}^{\vec{q},\lambda}(\mathbb{R}^{n})\) function \(b\) on mixed \(\lambda\)-central Morrey space \(\mathcal{B}^{\vec{q},\lambda}(\mathbb{R}^{n})\), respectively.
A bound on chaos Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas
The journal of high energy physics,
08/2016, Letnik:
2016, Številka:
8
Journal Article
Recenzirano
Odprti dostop
A
bstract
We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order ...correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ
L
≤ 2π
k
B
T/
ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.
The conformal extension of the BMS_{3} algebra is constructed. Apart from an infinite number of "superdilatations," in order to incorporate superspecial conformal transformations, the commutator of ...the latter with supertranslations strictly requires the presence of nonlinear terms in the remaining generators. The algebra appears to be very rigid, in the sense that its central extensions as well as the coefficients of the nonlinear terms become determined by the central charge of the Virasoro subalgebra. The wedge algebra corresponds to the conformal group in three spacetime dimensions SO(3,2), so that the full algebra can also be interpreted as an infinite-dimensional nonlinear extension of the AdS_{4} algebra with nontrivial central charges. Moreover, since the Lorentz subalgebra sl(2,R) is nonprincipally embedded within the conformal (wedge) algebra, according to the conformal weight of the generators, the conformal extension of BMS_{3} can be further regarded as a W_{(2,2,2,1)} algebra. An explicit canonical realization of the conformal extension of BMS_{3} is then shown to emerge from the asymptotic structure of conformal gravity in three dimensions, endowed with a new set of boundary conditions. The supersymmetric extension is also briefly addressed.
In this paper, we introduce the notion of a quasi-powerful p-group for odd primes p. These are the finite p-groups G such that Image omitted is powerful in the sense of Lubotzky and Mann. We show ...that this large family of groups shares many of the same properties as powerful p-groups. For example, we show that they have a regular power structure, and we generalise a result of Fernández-Alcober on the order of commutators in powerful p-groups to this larger family of groups. We also obtain a bound on the number of generators of a subgroup of a quasi-powerful p-group, expressed in terms of the number of generators of the group, and we give an example which demonstrates this bound is close to best possible.
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