Onset of synchronization in networks of second-order Kuramoto oscillators with delayed coupling: Exact results and application to phase-locked loops
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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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Results for “quantum statistical mechanics”
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On the theory of nonhomogeneous nonequilibrium superconductivity in 2D systems with massless fermions
Here we analyze static and nonequilibrium superconducting properties of a 2D relativistic-like model system with local electron-electron interaction, Rashba spin-orbit interaction αR in presence of time-dependent in-plane magnetic field H(t). It is shown that similar to the 2D case with ordinary massive quasiparticle dispersion ε(k)~|k| 2 at large fields, such a system demonstrates a nonhomogeneous superconducting stripe phase with the order parameter Δ(r)=Δ(0)cos(2[μ B B×r]n/$\hbarυ_F$) (B is the magnetic induction, υF is the Fermi velocity, n is the normal to the plane, μ B is the Bohr magneton, and αR$\ll$υF) where the stripes are oriented along the B direction. In the considered system, the inter-stripe period L and the magnitude of the magnetic field B are related by a universal relation BL=$\hbarυ_F$/μ B ≃0.714∙10 -4 Tm. Contrary to the case of massive quasiparticles, where the condition α R ~υ F can be, in principle, satisfied by increasing α R or by charge doping (Fermi velocity decreasing), in a relativistic-like system, where υF is doping-independent and one-two orders of magnitude larger than typical Fermi velocity in the “standard” 2D systems, the stripe phase can be the ground state at a rather low doping level. We also analyzed the nonequilibrium properties of the system with a focus on the melting of the stripe order (when the magnetic field is quenched to a lower value) and stripe dynamics (when the field is rotated by 90° degrees) and found several notable results. In particular, it was shown that the stripe domains melt according to law R~1$\sqrt{t}$ at initial times, while at longer times they shrink exponentially. In the case of the flipped magnetic field, the stripe orientation gradually turns from x- to y-direction, and the intermediate “crossed-stripe” phase takes place during times of order of picoseconds. Such a crossed phase is built of periodic superconducting bubbles that potentially may have applications in modern ultrafast superconducting technologies.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems
The dynamics of Markovian open quantum systems are described by Lindblad master equations. For fermionic and bosonic systems that are quasi-free, i.e. with Hamiltonians that are quadratic in the ladder operators and Lindblad operators that are linear in the ladder operators, we derive the equation of motion for the covariance matrix. This determines the evolution of Gaussian initial states and the steady states, which are also Gaussian. Using ladder super-operators (a.k.a. third quantization), here we show how the Liouvillian can be transformed to a many-body Jordan normal form which also reveals the full many-body spectrum. Extending previous work by Prosen and Seligman, we treat fermionic and bosonic systems on equal footing with Majorana operators, shorten and complete some derivations, also address the odd-parity sector for fermions, give a criterion for the existence of bosonic steady states, cover non-diagonalizable Liouvillians also for bosons, and include quadratic systems. In extension of the quasi-free open systems, quadratic open systems comprise additional Hermitian Lindblad operators that are quadratic in the ladder operators. While Gaussian states may then evolve into non-Gaussian states, the Liouvillian can still be transformed to a useful block-triangular form, and the equations of motion for k-point Green’s functions form a closed hierarchy. Based on this formalism, results on criticality and dissipative phase transitions in such models are discussed in a companion paper.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
An under-approximation of entropy for elemental multiconfigurational ground state electronic structures
A combinatorial approach has been applied to the allowable permutations of quantum electronic configurations under the constraints of Hund's rule for established ground state configurations toward an under-approximation of electronic structure entropy. Combined with a previously reported over-approximation, the approximations are used in conjunction in an attempt to bracket the upper and lower entropy limits for multiconfigurational ground state electronic structure entropy and compared to known standard molar entropies for the elements. This formality has been used for the application of a classical statistical mechanics methodology to be applied to the discrete sets of quantum mechanical states of Pu in order to calculate orbital occupancies in Pu's multiconfigurational ground state. Without consideration of the relative energies of various possible electronic configurations contributing to the multiconfigurational ground state, the calculations are performed under a general energy degeneracy assumption weighted to the number of permutations for specific configurations. The number of configurations assumed to significantly contribute is gradually constrained in order to approach a low-order approximation of orbital occupancies in Pu that are then compared to experimental and other calculated results from the literature.
Beaux, II, Miles F. (ORCID:000000032192626X)↗
Transient work function gating: A new photoemission regime
We present the theoretical basis for a new photoemission regime, transient work function gating (TWFG), which temporally and energetically gates photoemission and produces near-threshold photoelectrons with thermally limited emittance, percent-level quantum efficiency, and control over temporal coherence. The technique consists of actively gating the work function of a generalized photocathode using a non-ionizing long-wavelength optical field to produce an adiabatic modulation of the carrier density at their surface. We examine TWFG as a means to circumvent the long-standing trade-off between low emittance and high quantum efficiency, untethered to particle source or photocathode specifics. TWFG promises new opportunities in photoemission physics for next generation electron and accelerator-based x-ray photon sources.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
The quantum p -spin glass model: a user manual for holographers
We study a large-N bosonic quantum mechanical sigma-model with a spherical target space subject to disordered interactions, more colloquially known as the p-spin spherical model. Replica symmetry is broken at low temperatures and for sufficiently weak quantum fluctuations, which drives the system into a spin glass (SG) phase. The first half of this paper is dedicated to a discussion of this model's thermodynamics, with particular emphasis on the marginally stable SG. This phase exhibits an emergent conformal symmetry in the strong coupling regime, which dictates its thermodynamic properties. It is associated with an extensive number of nearby states in the free energy landscape. We discuss in detail an elegant approximate solution to the SG equations, which interpolates between the conformal regime and an ultraviolet-complete short distance solution. In the second half of this paper we explore the real-time dynamics of the model and uncover quantum chaos as measured by out-of-time-order four-point functions, both numerically and analytically. We find exponential Lyapunov growth, which intricately depends on the model's couplings and becomes strongest in the quantum critical regime. We emphasize that the SG phase also exhibits quantum chaos, albeit with parametrically smaller Lyapunov exponent than in the replica symmetric phase. An analytical calculation in the marginal SG phase suggests that this Lyapunov exponent vanishes in a particular infinite coupling limit. Finally, we comment on the potential meaning of these observations from the perspective of holography.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Quantum fluctuations drive nonmonotonic correlations in a qubit lattice
Abstract Fluctuations may induce the degradation of order by overcoming ordering interactions, consequently leading to an increase of entropy. This is particularly evident in magnetic systems characterized by nontrivial, constrained disorder, where thermal or quantum fluctuations can yield counterintuitive forms of ordering. Using the proven efficiency of quantum annealers as programmable spin system simulators, we present a study based on entropy postulates and experiments on a platform of programmable superconducting qubits to show that a low level of uncertainty can promote ordering in a system impacted by both thermal and quantum fluctuations. A set of experiments is proposed on a lattice of interacting qubits arranged in a triangular geometry with precisely controlled disorder, effective temperature, and quantum fluctuations. Our results demonstrate the creation of ordered ferrimagnetic and layered anisotropic disordered phases, displaying characteristics akin to the elegant order-by-disorder phenomenon. Extensive experimental evidence is provided for the role of quantum fluctuations in lowering the total energy of the system by increasing entropy and defect clustering. Our thorough and comprehensive application of an intentionally introduced noise on a quantum platform provides insight into the dynamics of defects and fluctuations in quantum devices, which may help to reduce the cost associated with quantum processing.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Generalized Wigner theorem for noninvertible symmetries
In this article, we establish the conditions under which a conservation law associated with a non-invertible operator may be realized as a symmetry in quantum physics. As established by Wigner, all quantum symmetries must be represented by either unitary or antiunitary transformations. Relinquishing an implicit assumption of invertibility, we demonstrate that the fundamental invariance of quantum transition probabilities under the application of symmetries mandates that all non-invertible symmetries may only correspond to projective unitary or antiunitary transformations, i.e., partial isometries. This extends the notion of physical states beyond conventional rays in Hilbert space to equivalence classes in an extended, gauged Hilbert space, thereby broadening the traditional understanding of symmetry transformations in quantum theory. Our generalized theorem applies irrespective of the origin of the (non)invertible symmetry, holds in arbitrary spatial dimensions, and is independent of the Hamiltonian or action. We explore its physical consequences and, using simple model systems, illustrate how the distinction between invertible and non-invertible symmetries can sometimes be tied to the choice of boundary conditions.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Deviations from maximal entanglement for eigenstates of the Sachdev-Ye-Kitaev model
We consider mid-spectrum eigenstates of the Sachdev-Ye-Kiteav (SYK) model. We prove that for subsystems whose size is a constant fraction of the system size, the entanglement entropy deviates from the maximum entropy by at least a positive constant. This result highlights the difference between the entanglement entropy of mid-spectrum eigenstates of the SYK model and that of random states.
Disordered Systems and Neural Networks (cond-mat.d↗
Scrambling Dynamics with Imperfections in a Solvable Model
We study how probes of quantum scrambling dynamics respond to two kinds of imperfections -- unequal forward and backward evolutions and decoherence -- in a solvable Brownian circuit model. We calculate a ``renormalized'' out-of-time-order correlator (ROTOC) in the model with $N$ qubits, and we show that the circuit-averaged ROTOC is controlled by an effective probability distribution in operator weight space which obeys a system of $N$ non-linear equations of motion. These equations can be easily solved numerically for large system sizes which are beyond the reach of exact methods. Moreover, for an operator initially concentrated on weight one $w_0=1$, we provide an exact solution to the equations in the thermodynamic limit of many qubits that is valid for all times, all non-vanishing perturbation strengths $p\gtrsim 1/\sqrt{N}$, and all decoherence strengths. We also show that a generic initial condition $w_0 >1$ leads to a metastable state that eventually collapses to the $w_0=1$ case after a lifetime $\sim \log(N/w_0)$. Our results highlight situations where it is still possible to extract the unperturbed chaos exponent even in the presence of imperfections, and we comment on the applications of our results to existing experiments with nuclear spins and to future scrambling experiments.
FOS: Physical sciences↗
Tightening the thermodynamic uncertainty relations with null-entropy events: What we learn when nothing happens
Fluctuation theorems establish that thermodynamic processes at the microscale can occasionally result in negative entropy production. At the microscale, another distinct possibility becomes more likely: processes where no entropy is produced overall. In this work, we explore the constraints imposed by such null-entropy events on the fluctuations of thermodynamic currents. By incorporating the probability of null-entropy events, we obtain tighter bounds on finite-time thermodynamic uncertainty relations derived from fluctuation theorems. We validate this framework using an example of a qudit SWAP engine.
FOS: Physical sciences↗
Infinite temperature at zero energy
We construct a family of static, geometrically local Hamiltonians that inherit eigenstate properties of periodically-driven (Floquet) systems. Our construction is a variation of the Feynman-Kitaev clock -- a well-known mapping between quantum circuits and local Hamiltonians -- where the clock register is given periodic boundary conditions. Assuming the eigenstate thermalization hypothesis (ETH) holds for the input circuit, our construction yields Hamiltonians whose eigenstates have properties characteristic of infinite temperature, like volume-law entanglement entropy, across the whole spectrum -- including the ground state. We then construct a family of exactly solvable Floquet quantum circuits whose eigenstates are shown to obey the ETH at infinite temperature. Combining the two constructions yields a new family of local Hamiltonians with provably volume-law-entangled ground states, and the first such construction where the volume law holds for all contiguous subsystems.
FOS: Physical sciences↗
Diffusion Codes: Self-Correction from Small(er)-Set Expansion with Tunable Non-locality
Optimal constructions of classical LDPC codes can be obtained by choosing the Tanner graph uniformly at random among biregular graphs. We introduce a class of codes that we call ``diffusion codes'', defined by placing each edge connecting bits and checks on some graph, and acting on that graph with a random SWAP network. By tuning the depth of the SWAP network, we can tune a tradeoff between the amount of randomness -- and hence the optimality of code parameters -- and locality with respect to the underlying graph. For diffusion codes defined on the cycle graph, if the SWAP network has depth $\sim Tn$ with $T> n^{2β}$ for arbitrary $β>0$, then we prove that almost surely the Tanner graph is a lossless ``smaller set'' vertex expander for small sets up size $δ\sim \sqrt T \sim n^β$, with bounded bit and check degree. At the same time, the geometric size of the largest stabilizer is bounded by $\sqrt T$ in graph distance. We argue, based on physical intuition, that this result should hold more generally on arbitrary graphs. By taking hypergraph products of these classical codes we obtain quantum LDPC codes defined on the torus with smaller-set boundary and co-boundary expansion and the same expansion/locality tradeoffs as for the classical codes. These codes are self-correcting and admit single-shot decoding, while having the geometric size of the stabilizer growing as an arbitrarily small power law. Our proof technique establishes mixing of a random SWAP network on small subsystems at times scaling with only the subsystem size, which may be of independent interest.
Combinatorics (math.CO)↗
Lieb-Robinson Light Cone for Power-Law Interactions
The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as 1 / r α at distance r ? Here, we present a definitive answer to this question for all exponents α > 2 d and all spatial dimensions d . Schematically, information takes time at least r min { 1 , α - 2 d } to propagate a distance r . As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A principle of maximum ignorance for semiclassical gravity
The principle of maximum ignorance posits that the coarse-grained description of a system is maximally agnostic about its underlying microscopic structure. We briefly review this principle for random matrix theory and for the eigenstate thermalization hypothesis. We then apply this principle in holography to construct ensembles of random mixed states. This leads to an ensemble of microstates which models our microscopic ignorance, and which on average reproduces the effective semiclassical physics of a given bulk state. We call this ensemble the state-averaging ansatz. The output of our model is a prediction for semiclassical contributions to variances and higher statistical moments over the ensemble of microstates. The statistical moments provide coarse-grained — yet gravitationally non-perturbative — information about the microstructure of the individual states of the ensemble. We show that these contributions exactly match the on-shell action of known wormhole configurations of the gravitational path integral. These results strengthen the view that wormholes simply parametrize the ignorance of the microstructure of a fundamental state, given a fixed semiclassical bulk description.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Entanglement transitions from restricted Boltzmann machines
The search for novel entangled phases of matter has lead to the recent discovery of a new class of “en- tanglement transitions,” exemplified by random tensor networks and monitored quantum circuits. Most known examples can be understood as some classical ordering transitions in an underlying statistical mechanics model, where entanglement maps onto the free-energy cost of inserting a domain wall. In this paper we study the possibility of entanglement transitions driven by physics beyond such statistical mechanics mappings. Motivated by recent applications of neural-network-inspired variational Ansätze, we investigate under what conditions on the variational parameters these Ansätze can capture an entanglement transition. We study the entanglement scaling of short-range restricted Boltzmann machine (RBM) quantum states with random phases. For uncorrelated random phases, we analytically demonstrate the absence of an entanglement transition and reveal subtle finite-size effects in finite-size numerical simulations. Introducing phases with correlations decaying as 1/r α in real space, we observe three regions with a different scaling of entanglement entropy depending on the exponent α. We study the nature of the transition between these regions, finding numerical evidence for critical behavior. Furthermore, our work establishes the presence of long-range correlated phases in RBM-based wave functions as a required ingredient for entanglement transitions.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Statistical Significance Testing for Mixed Priors: A Combined Bayesian and Frequentist Analysis
In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it incorporates Occam’s razor via the multiplicity or trials factor in the look-elsewhere effect. However, if the prior is not known completely, the frequentist hypothesis test via the false-positive rate is a better approach, as it is less sensitive to the prior choice. We argue that when only partial prior information is available, it is best to combine the two methodologies by using the Bayes factor as a test statistic in the frequentist analysis. We show that the standard frequentist maximum likelihood-ratio test statistic corresponds to the Bayes factor with a non-informative Jeffrey’s prior. We also show that mixed priors increase the statistical power in frequentist analyses over the maximum likelihood test statistic. We develop an analytic formalism that does not require expensive simulations and generalize Wilks’ theorem beyond its usual regime of validity. In specific limits, the formalism reproduces existing expressions, such as the p-value of linear models and periodograms. We apply the formalism to an example of exoplanet transits, where multiplicity can be more than 10 7 . We show that our analytic expressions reproduce the $p$-values derived from numerical simulations. We offer an interpretation of our formalism based on the statistical mechanics. We introduce the counting of states in a continuous parameter space using the uncertainty volume as the quantum of the state. We show that both the $p$-value and Bayes factor can be expressed as an energy versus entropy competition.
97 MATHEMATICS AND COMPUTING↗
On the generalised equipartition law
We observe that the so-called Generalised Equipartition Law for hamiltonian systems is actually valid only under specific hypotheses – unfortunately omitted in some textbooks – which limit its applicability when dealing with nonlinear systems. We introduce a new coordinate-independent generalisation which overcomes this problem and can be applied to a larger set of functions. A simple example of application is discussed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗