Operator Growth Bounds from Graph Theory Chen, Chi-Fang; Lucas, Andrew
Communications in mathematical physics,
08/2021, Letnik:
385, Številka:
3
Journal Article
Recenzirano
Odprti dostop
Let
A
and
B
be local operators in Hamiltonian quantum systems with
N
degrees of freedom and finite-dimensional Hilbert space. We prove that the commutator norm
‖
A
(
t
)
,
B
‖
is upper bounded by a ...topological combinatorial problem: counting irreducible weighted paths between two points on the Hamiltonian’s factor graph. Our bounds sharpen existing Lieb–Robinson bounds by removing extraneous growth. In quantum systems drawn from zero-mean random ensembles with few-body interactions, we prove stronger bounds on the ensemble-averaged out-of-time-ordered correlator
E
‖
A
(
t
)
,
B
‖
F
2
. In such quantum systems on Erdös–Rényi factor graphs, we prove that the scrambling time
t
s
, at which
‖
A
(
t
)
,
B
‖
F
=
Θ
(
1
)
, is almost surely
t
s
=
Ω
(
log
N
)
; we further prove
t
s
=
Ω
(
log
N
)
to high order in perturbation theory in 1/
N
. We constrain infinite temperature quantum chaos in the
q
-local Sachdev-Ye-Kitaev model at any order in 1/
N
; at leading order, our upper bound on the Lyapunov exponent is within a factor of 2 of the known result at any
q
>
2
. We also speculate on the implications of our theorems for conjectured holographic descriptions of quantum gravity.
In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed ...of light. Local operations at sufficiently separated spacetime points approximately commute—given a many-body state|ψ⟩,Ox(t)Oy|ψ⟩≈OyOx(t)|ψ⟩with arbitrarily small errors—so long as|x−y|≳vt, wherevis finite. Yet, most nonrelativistic physical systems realized in nature have long-range interactions: Two degrees of freedom separated by a distancerinteract with potential energyV(r)∝1/rα. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: At the sameα, some quantum information processing tasks are constrained by a linear light cone, while others are not. In one spatial dimension, this linear light cone exists for every many-body state|ψ⟩whenα>3(Lieb-Robinson light cone); for a typical state|ψ⟩chosen uniformly at random from the Hilbert space whenα>52(Frobenius light cone); and for every state of a noninteracting system whenα>2(free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones—and their tightness—also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, is bounded by the Frobenius light cone and, therefore, is poorly constrained by all Lieb-Robinson bounds.
Weight management is highly recommended to patients with diabetes mellitus. However, this prescription is often characterized by weight fluctuations. It remains unclear the effects of weight ...fluctuations on outcomes in diabetes mellitus. We used the public use dataset from the Action to Control Cardiovascular Risk in Diabetes (ACCORD) trial to assess the effects of baseline weight, change in weight, and body weight variability (BWV) on outcomes. The ACCORD trial participant's weights were documented annually during the trial. Our primary predictor variables were baseline weight, change in body weight (Initial – final) and BWV defined as average successive variability in weight (average absolute difference between successive values) during the trial. Cox proportional hazards model was used. Out of the 10,251 ACCORD participants, 911(8.9%), 2985(29.1%), and 6355(62%) were normal weight, overweight, and obese. After a mean of 3.5 years of follow-up, 10.2% had the primary outcome (nonfatal MI or nonfatal stroke or CV death), 4.3% had heart failure, 7% died, and 60.7% reported a microvascular complication. BWV was associated with the primary outcome, heart failure, death, and microvascular events in our full models which included BMI HR (95%CI): 1.25(1.15 to 1.36), 1.59(1.45 to 1.75), 1.74(1.63 to 1.85) and 1.18(1.13 to 1.22), p < 0.0001 respectively). Participants who died were in the quartile that gained the most weight. In this post hoc analysis of ACCORD trial, body weight variability was significantly associated with poor outcomes independent of CVD risk factors and BMI. Our study is consistent with significant risk associated with weight fluctuations in patients with diabetes mellitus.
Abstract
Among the top customer complaints regarding retailers are experiences of exclusionary treatment in the form of explicit condescension or implicit disregard. However, little is known about ...how consumers respond to different instances of exclusion in retail or service settings. This research focuses on how customers respond cognitively and emotionally when frontline staff reject or ignore them and on how retailers can recover from such service failures. Findings from six studies using exclusion as a hypothetical scenario or a real experience demonstrate that direct negative feedback leads customers to feel rejected and to form concrete low-level mental construals, while a lack of attention leads customers to feel ignored and to form abstract high-level construals. Explicit rejection (implicit ignoring) causes consumers to form more (less) vivid mental imagery of the exclusionary experience and to activate a concrete (abstract) mindset, resulting in preferences for tangible (intangible) and visual (textual) compensation options. Retailers are advised to align their compensation with construal levels to increase post-recovery customer satisfaction, customer reviews, intended loyalty, and brand referral behavior.
Abstract
The authors review the marketing practices likely to make customers feel excluded (ignored or rejected) and analyze the potency of retail exclusion in the transforming service encounters due ...to the infusion of artificial intelligence (AI), robots, and other new technologies. Synthesizing the findings of prior studies, the authors propose an integrative theoretical framework for understanding different perspectives, psychological mechanisms, and outcomes of retail exclusion, and highlight research opportunities for retail exclusion in two contexts of service encounters: interpersonal and technology‐powered. The review aims to provide implications on proactive strategies to minimize the adverse effects of retail exclusions and promote inclusive customer experiences.
Causal attributions and brand-relationships are known to determine how consumers react to brand transgressions. Considering both transgression controllability and brand-relationship strength, the ...authors show that self-construal moderates consumer reactions to brand transgressions. Three studies using different product and service failure scenarios demonstrate that consumers who have independent self-construals are more forgiving when the brand has no control over the transgression, regardless of brand-relationship strength. However, consumers who have interdependent self-construals are more forgiving when they have strong relationships with the transgressing brand, even if the brand is at fault. Furthermore, the salience of justice concerns versus expectancies for long-term brand-relationships underlies the self-construal effects on consumer forgiveness.
At zero temperature, the charge current operator appears to be conserved, within linear response, in certain holographic probe brane models of strange metals. At small but finite temperature, we ...analytically show that the weak non-conservation of this current leads to both a collective “zero sound” mode and a Drude peak in the electrical conductivity. This simultaneously resolves two outstanding puzzles about probe brane theories. The nonlinear dynamics of the current operator itself appears qualitatively different.
Cryptococcus neoformans is a ubiquitous environmental fungus that can cause life-threatening meningitis and fungemia, often in the presence of acquired immunodeficiency syndrome (AIDS), liver ...cirrhosis, diabetes mellitus, or other medical conditions. To distinguish risk factors from comorbidities, we performed a hospital-based, density-sampled, matched case-control study.
All new-onset cryptococcal meningitis cases and cryptococcemia cases at a university hospital in Taiwan from 2002-2010 were retrospectively identified from the computerized inpatient registry and were included in this study. Controls were selected from those hospitalized patients not experiencing cryptococcal meningitis or cryptococcemia. Controls and cases were matched by admission date, age, and gender. Conditional logistic regression was used to analyze the risk factors.
A total of 101 patients with cryptococcal meningitis (266 controls) and 47 patients with cryptococcemia (188 controls), of whom 32 patients had both cryptococcal meningitis and cryptococcemia, were included in this study. Multivariate regression analysis showed that AIDS (adjusted odds ratio aOR = 181.4; p < 0.001), decompensated liver cirrhosis (aOR = 8.5; p = 0.008), and cell-mediated immunity (CMI)-suppressive regimens without calcineurin inhibitors (CAs) (aOR = 15.9; p < 0.001) were independent risk factors for cryptococcal meningitis. Moreover, AIDS (aOR = 216.3, p < 0.001), decompensated liver cirrhosis (aOR = 23.8; p < 0.001), CMI-suppressive regimens without CAs (aOR = 7.3; p = 0.034), and autoimmune diseases (aOR = 9.3; p = 0.038) were independent risk factors for developing cryptococcemia. On the other hand, diabetes mellitus and other medical conditions were not found to be risk factors for cryptococcal meningitis or cryptococcemia.
The findings confirm AIDS, decompensated liver cirrhosis, CMI-suppressive regimens without CAs, and autoimmune diseases are risk factors for invasive C. neoformans diseases.
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