Domain Wall Dynamics in Classical Spin Chains: Free Propagation, Subdiffusive Spreading, and Soliton Emission.

The nonequilibrium dynamics of domain wall initial states in a classical anisotropic Heisenberg chain exhibits a striking coexistence of apparently linear and nonlinear behaviors: the propagation and spreading of the domain wall can be captured quantitatively by linear, i.e., noninteracting, spin wave theory absent its usual justifications; while, simultaneously, for a wide range of easy-plane anisotropies, emission can take the place of stable solitons-a process and objects intrinsically associated with interactions and nonlinearities. The easy-axis domain wall only has transient dynamics, the isotropic one broadens diffusively, while the easy-plane one yields a pair of ballistically counterpropagating domain walls which, unusually, broaden subdiffusively, their width scaling as t^{1/3}.

Random sparse generators of Markovian evolution and their spectral properties.

The evolution of a complex multistate system is often interpreted as a continuous-time Markovian process. To model the relaxation dynamics of such systems, we introduce an ensemble of random sparse matrices which can be used as generators of Markovian evolution. The sparsity is controlled by a parameter φ, which is the number of nonzero elements per row and column in the generator matrix. Thus, a member of the ensemble is characterized by the Laplacian of a directed regular graph with D vertices (number of system states) and 2φD edges with randomly distributed weights. We study the effects of sparsity on the spectrum of the generator. Sparsity is shown to close the large spectral gap that is characteristic of nonsparse random generators. We show that the first moment of the eigenvalue distribution scales as ∼φ, while its variance is ∼sqrt[φ]. By using extreme value theory, we demonstrate how the shape of the spectral edges is determined by the tails of the corresponding weight distributions and clarify the behavior of the spectral gap as a function of D. Finally, we analyze complex spacing ratio statistics of ultrasparse generators, φ=const, and find that starting already at φ⩾2, spectra of the generators exhibit universal properties typical of Ginibre's orthogonal ensemble.

Entropy and temperature in finite isolated quantum systems.

We investigate how the temperature calculated from the microcanonical entropy compares with the canonical temperature for finite isolated quantum systems. We concentrate on systems with sizes that make them accessible to numerical exact diagonalization. We thus characterize the deviations from ensemble equivalence at finite sizes. We describe multiple ways to compute the microcanonical entropy and present numerical results for the entropy and temperature computed in these various ways. We show that using an energy window whose width has a particular energy dependence results in a temperature with minimal deviations from the canonical temperature.

Assigning temperatures to eigenstates.

In the study of thermalization in finite isolated quantum systems, an inescapable issue is the definition of temperature. We examine and compare different possible ways of assigning temperatures to energies or equivalently to eigenstates in such systems. A commonly used assignment of temperature in the context of thermalization is based on the canonical energy-temperature relationship, which depends only on energy eigenvalues and not on the structure of eigenstates. For eigenstates, we consider defining temperature by minimizing the distance between (full or reduced) eigenstate density matrices and canonical density matrices. We show that for full eigenstates, the minimizing temperature depends on the distance measure chosen and matches the canonical temperature for the trace distance; however, the two matrices are not close. With reduced density matrices, the minimizing temperature has fluctuations that scale with subsystem and system size but appears to be independent of distance measure. In particular limits, the two matrices become equivalent while the temperature tends to the canonical temperature.

Chaos in the three-site Bose-Hubbard model: Classical versus quantum.

We consider a quantum many-body system-the Bose-Hubbard system on three sites-which has a classical limit, and which is neither strongly chaotic nor integrable but rather shows a mixture of the two types of behavior. We compare quantum measures of chaos (eigenvalue statistics and eigenvector structure) in the quantum system, with classical measures of chaos (Lyapunov exponents) in the corresponding classical system. As a function of energy and interaction strength, we demonstrate a strong overall correspondence between the two cases. In contrast to both strongly chaotic and integrable systems, the largest Lyapunov exponent is shown to be a multivalued function of energy.

Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles.

Eigenstates of local many-body interacting systems that are far from spectral edges are thought to be ergodic and close to being random states. This is consistent with the eigenstate thermalization hypothesis and volume-law scaling of entanglement. We point out that systematic departures from complete randomness are generically present in midspectrum eigenstates, and focus on the departure of the entanglement entropy from the random-state prediction. We show that the departure is (partly) due to spatial correlations and due to orthogonality to the eigenstates at the spectral edge, which imposes structure on the midspectrum eigenstates.

Long-lived solitons and their signatures in the classical Heisenberg chain.

Motivated by the Kardar-Parisi-Zhang (KPZ) scaling recently observed in the classical ferromagnetic Heisenberg chain, we investigate the role of solitonic excitations in this model. We find that the Heisenberg chain, although well known to be nonintegrable, supports a two-parameter family of long-lived solitons. We connect these to the exact soliton solutions of the integrable Ishimori chain with ln(1+S_{i}·S_{j}) interactions. We explicitly construct infinitely long-lived stationary solitons, and provide an adiabatic construction procedure for moving soliton solutions, which shows that Ishimori solitons have a long-lived Heisenberg counterpart when they are not too narrow and not too fast moving. Finally, we demonstrate their presence in thermal states of the Heisenberg chain, even when the typical soliton width is larger than the spin correlation length, and argue that these excitations likely underlie the KPZ scaling.

Eigenstate thermalization scaling in approaching the classical limit.

According to the eigenstate thermalization hypothesis (ETH), the eigenstate-to-eigenstate fluctuations of expectation values of local observables should decrease with increasing system size. In approaching the thermodynamic limit-the number of sites and the particle number increasing at the same rate-the fluctuations should scale as ∼D^{-1/2} with the Hilbert space dimension D. Here, we study a different limit-the classical or semiclassical limit-by increasing the particle number in fixed lattice topologies. We focus on the paradigmatic Bose-Hubbard system, which is quantum-chaotic for large lattices and shows mixed behavior for small lattices. We derive expressions for the expected scaling, assuming ideal eigenstates having Gaussian-distributed random components. We show numerically that, for larger lattices, ETH scaling of physical midspectrum eigenstates follows the ideal (Gaussian) expectation, but for smaller lattices, the scaling occurs via a different exponent. We examine several plausible mechanisms for this anomalous scaling.

Many-Body Quantum Dynamics of Initially Trapped Systems due to a Stark Potential: Thermalization versus Bloch Oscillations.

We analyze the dynamics of an initially trapped cloud of interacting quantum particles on a lattice under a linear (Stark) potential. We reveal a dichotomy: initially trapped interacting systems possess features typical of both many-body-localized and thermalizing systems. We consider both fermions (t-V model) and bosons (Bose-Hubbard model). For the zero and infinite interaction limits, both systems are integrable: we provide analytic solutions in terms of the moments of the initial cloud shape and clarify how the recurrent dynamics (many-body Bloch oscillations) depends on the initial state. Away from the integrable points, we identify and explain the timescale at which Bloch oscillations decohere.

Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems.

Multifractal dimensions allow for characterizing the localization properties of states in complex quantum systems. For ergodic states the finite-size versions of fractal dimensions converge to unity in the limit of large system size. However, the approach to the limiting behavior is remarkably slow. Thus, an understanding of the scaling and finite-size properties of fractal dimensions is essential. We present such a study for random matrix ensembles, and compare with two chaotic quantum systems-the kicked rotor and a spin chain. For random matrix ensembles we analytically obtain the finite-size dependence of the mean behavior of the multifractal dimensions, which provides a lower bound to the typical (logarithmic) averages. We show that finite statistics has remarkably strong effects, so that even random matrix computations deviate from analytic results (and show strong sample-to-sample variation), such that restoring agreement requires exponentially large sample sizes. For the quantized standard map (kicked rotor) the multifractal dimensions are found to follow the random matrix predictions closely, with the same finite statistics effects. For a XXZ spin-chain we find significant deviations from the random matrix prediction-the large-size scaling follows a system-specific path towards unity. This suggests that local many-body Hamiltonians are "weakly ergodic," in the sense that their eigenfunction statistics deviate from random matrix theory.

Sexually dimorphic oxytocin receptor-expressing neurons in the preoptic area of the mouse brain.

Oxytocin is involved in the regulation of social behaviors including parental behaviors in a variety of species. Oxytocin triggers social behaviors by binding to oxytocin receptors (OXTRs) in various parts of the brain. OXTRs are present in the preoptic area (POA) where hormone-sensitive sexually dimorphic nuclei exist. The present study was conducted to examine whether sex differences exist in the distribution of neurons expressing OXTRs in the POA. Using OXTR-Venus (an enhanced variant of yellow fluorescent protein) mice, the distribution of OXTR-Venus cells in the POA was compared between sexes. The total number of OXTR-Venus cells in the medial POA (MPOA) was significantly greater in females than in males. No detectable OXTR-Venus cells were observed in the anteroventral periventricular nucleus (AVPV) within the MPOA in most of the brain sections from males. We further examined the total number of OXTR-Venus cells in the AVPV and the rest of the MPOA between the sexes. The total number of OXTR-Venus cells in the AVPV in females (615 ± 43) was significantly greater than that in males (14 ± 2), whereas the total number of OXTR-Venus cells in the rest of the MPOA did not differ significantly between the sexes. Thus, the sexually dimorphic expression of OXTR-Venus specifically occurred in the AVPV, but not in the rest of the MPOA. We also examined whether the expression of OXTR in the AVPV is driven by the female gonadal hormone, estrogen. Immunocytochemistry and single-cell RT-PCR revealed the presence of the estrogen receptor α in OXTR-Venus cells in the female AVPV. Moreover, ovariectomy resulted in the absence of OXTR-Venus expression in the AVPV, whereas estrogen replacement therapy restored OXTR-Venus expression. These results demonstrate that the expression of OXTR in the AVPV is primarily female specific and estrogen dependent. The presence of the sexually dimorphic expression of OXTR in the AVPV suggests the involvement of OXTR neurons in the AVPV in the regulation of female-specific behavior and/or physiology.

Eigenstate Thermalization, Random Matrix Theory, and Behemoths.

The eigenstate thermalization hypothesis (ETH) is one of the cornerstones of contemporary quantum statistical mechanics. The extent to which ETH holds for nonlocal operators is an open question that we partially address in this Letter. We report on the construction of highly nonlocal operators, behemoths, that are building blocks for various kinds of local and nonlocal operators. The behemoths have a singular distribution and width w∼D^{-1} (D being the Hilbert space dimension). From there, one may construct local operators with the ordinary Gaussian distribution and w∼D^{-1/2} in agreement with ETH. Extrapolation to even larger widths predicts sub-ETH behavior of typical nonlocal operators with w∼D^{-δ}, 0<δ<1/2. This operator construction is based on a deep analogy with random matrix theory and shows striking agreement with numerical simulations of nonintegrable many-body systems.

Aldosterone Mediated Regulation of Epithelial Sodium Channel (ENaC) Subunits in the Rat Hypothalamus.

Current evidence suggests that the epithelial Na+ channel (ENaC) in the brain plays a significant role in the development of hypertension. ENaC is present in vasopressin (VP) neurons in the hypothalamus, suggesting that ENaC in VP neurons is involved in the regulation of blood pressure. Our recent study demonstrated that high dietary salt intake caused an increase in the expression and activity of ENaC that were responsible for the more depolarized basal membrane potential in VP neurons. A known regulator of ENaC expression, the mineralocorticoid receptor (MR), is present in VP neurons, suggesting that ENaC expression in VP neurons is regulated by aldosterone. In this study, the effects of aldosterone and corticosterone on ENaC were examined in acute hypothalamic slices. Real-time PCR and Western blot analysis showed that aldosterone and corticosterone treatment resulted in a significant increase in the expression of γENaC, but not α- or ßENaC, and that this expression was attenuated by MR and glucocorticoid receptor (GR) antagonists. Moreover, chromatin immunoprecipitation demonstrated that the aldosterone-MR complex directly interacts with the promoter region of the γENaC gene. However, the treatment with aldosterone did not cause subcellular translocation of ENaC toward the plasma membrane nor an increase in ENaC Na+-leak current. These results indicate that expression of γENaC in VP neurons is induced by aldosterone and corticosterone through their MR and GR, respectively; however, aldosterone or corticosterone alone is not sufficient enough to increase ENaC current when they are applied to hypothalamic slices in vitro.

Statistical properties of eigenstate amplitudes in complex quantum systems.

We study the eigenstates of quantum systems with large Hilbert spaces, via their distribution of wave-function amplitudes in a real-space basis. For single-particle "quantum billiards," these real-space amplitudes are known to have Gaussian distribution for chaotic systems. In this work, we formulate and address the corresponding question for many-body lattice quantum systems. For integrable many-body systems, we examine the deviation from Gaussianity and provide evidence that the distribution generically tends toward power-law behavior in the limit of large sizes. We relate the deviation from Gaussianity to the entanglement content of many-body eigenstates. For integrable billiards, we find several cases where the distribution has power-law tails.

Polymer-mineral scaffold augments in vivo equine multipotent stromal cell osteogenesis.

BACKGROUND: Use of bioscaffolds to direct osteogenic differentiation of adult multipotent stromal cells (MSCs) without exogenous proteins is a contemporary approach to bone regeneration. Identification of in vivo osteogenic contributions of exogenous MSCs on bioscaffolds after long-term implantation is vital to understanding cell persistence and effect duration. METHODS: This study was designed to quantify in vivo equine MSC osteogenesis on synthetic polymer scaffolds with distinct mineral combinations 9 weeks after implantation in a murine model. Cryopreserved, passage (P)1, equine bone marrow-derived MSCs (BMSC) and adipose tissue-derived MSCs (ASC) were culture expanded to P3 and immunophenotyped with flow cytometry. They were then loaded by spinner flask on to scaffolds composed of tricalcium phosphate (TCP)/hydroxyapatite (HA) (40:60; HT), polyethylene glycol (PEG)/poly-L-lactic acid (PLLA) (60:40; GA), or PEG/PLLA/TCP/HA (36:24:24:16; GT). Scaffolds with and without cells were maintained in static culture for up to 21 days or implanted subcutaneously in athymic mice that were radiographed every 3 weeks up to 9 weeks. In vitro cell viability and proliferation were determined. Explant composition (double-stranded (ds)DNA, collagen, sulfated glycosaminoglycan (sGAG), protein), equine and murine osteogenic target gene expression, microcomputed tomography (µCT) mineralization, and light microscopic structure were assessed. RESULTS: The ASC and BMSC number increased significantly in HT constructs between 7 and 21 days of culture, and BMSCs increased similarly in GT constructs. Radiographic opacity increased with time in GT-BMSC constructs. Extracellular matrix (ECM) components and dsDNA increased significantly in GT compared to HT constructs. Equine and murine osteogenic gene expression was highest in BMSC constructs with mineral-containing scaffolds. The HT constructs with either cell type had the highest mineral deposition based on µCT. Regardless of composition, scaffolds with cells had more ECM than those without, and osteoid was apparent in all BMSC constructs. CONCLUSIONS: In this study, both exogenous and host MSCs appear to contribute to in vivo osteogenesis. Addition of mineral to polymer scaffolds enhances equine MSC osteogenesis over polymer alone, but pure mineral scaffold provides superior osteogenic support. These results emphasize the need for bioscaffolds that provide customized osteogenic direction of both exo- and endogenous MSCs for the best regenerative potential.

Collagen and Hydroxyapatite Scaffolds Activate Distinct Osteogenesis Signaling Pathways in Adult Adipose-Derived Multipotent Stromal Cells.

Osteogenic cell signaling pathway disruption varies among bone diseases. This investigation was designed to identify adipose-derived multipotent stromal cell (ASC) and bone graft scaffold combinations for local, targeted restoration of gene expression and extracellular matrix (ECM) deposition. Human ASC osteogenesis on bone graft materials was quantified following culture in stromal (S), osteogenic (O), or osteogenic for 48 h followed by stromal medium (OS) to test the two-part hypothesis: (1) identical ASC isolates on distinct bone graft scaffolds demonstrate unique viability, differentiation, ECM production, and gene expression in the same culture conditions; (2) identical ASC-bone graft scaffold combinations have different cell viability, differentiation, ECM production, and gene expression when cultured in S, O, or OS medium. Three commercially available bone graft scaffold materials, type I bovine collagen (C), hydroxyapatite + ß-tricalcium phosphate + type I bovine collagen (HT), and ß-tricalcium phosphate + type I bovine collagen (CT) were evaluated. Passage 3 ASCs were loaded onto scaffold blocks with a spinner flask bioreactor, and constructs were cultured up to 28 days. Cell viability, gene expression (alkaline phosphatase [ALPL], osteoprotegerin [TNFRSF11B], osteocalcin [BGLAP], cannabinoid receptors type I [CNR1] and II [CNR2], receptor activator of nuclear factor kappa ß ligand [TNFSF11]), as well as ECM DNA, collagen, sulfated glycosaminoglycan, and protein content were quantified. Matrix organization was evaluated with scanning electron microscopy. Effects of scaffold, medium, or culture duration on cell viability were minimal. Significantly higher initial ALPL expression decreased with time, while BGLAP expression increased in HT constructs in O medium, and the constructs had the most abundant ECM components and ultrastructural organization. There was a similar, although delayed, pattern of gene expression and greater ECM collagen with less organization in C constructs in O medium. Higher CNR1 expression in C versus higher TNFRSF11B/TNFSF11 expression in HT constructs throughout the study support stimulation of unique osteogenic signaling pathways by identical cell isolates. These results suggest that bone scaffold composition may be used to selectively target specific osteogenic cell signaling pathways in ASC constructs to stimulate ECM deposition based on therapeutic needs.

Effect of dietary salt intake on epithelial Na+ channels (ENaC) in vasopressin magnocellular neurosecretory neurons in the rat supraoptic nucleus.

KEY POINTS: A growing body of evidence suggests that epithelial Na+ channels (ENaCs) in the brain play a significant role in the regulation of blood pressure; however, the brain structures that mediate the effect are not well understood. Because vasopressin (VP) neurons play a pivotal role in coordinating neuroendocrine and autonomic responses to maintain cardiovascular homeostasis, a basic understanding of the regulation and activity of ENaC in VP neurons is of great interest. We show that high dietary salt intake caused an increase in the expression and activity of ENaC which resulted in the steady state depolarization of VP neurons. The results help us understand one of the mechanisms underlying how dietary salt intake affects the activity of VP neurons via ENaC activity. ABSTRACT: All three epithelial Na+ channel (ENaC) subunits (α, ß and γ) are located in vasopressin (VP) magnocellular neurons in the hypothalamic supraoptic (SON) and paraventricular nuclei. Our previous study demonstrated that ENaC mediates a Na+ leak current that affects the steady state membrane potential in VP neurons. In the present study, we evaluated the effect of dietary salt intake on ENaC regulation and activity in VP neurons. High dietary salt intake for 7 days caused an increase in expression of ß- and γENaC subunits in the SON and the translocation of αENaC immunoreactivity towards the plasma membrane. Patch clamp experiments on hypothalamic slices showed that the mean amplitude of the putative ENaC currents was significantly greater in VP neurons from animals that were fed a high salt diet compared with controls. The enhanced ENaC current contributed to the more depolarized basal membrane potential observed in VP neurons in the high salt diet group. These findings indicate that high dietary NaCl intake enhances the expression and activity of ENaCs, which augments synaptic drive by depolarizing the basal membrane potential close to the action potential threshold during hormonal demand. However, ENaCs appear to have only a minor role in the regulation of the firing activity of VP neurons in the absence of synaptic inputs as neither the mean intraburst frequency, burst duration, nor interspike interval variability of phasic bursting activity was affected. Moreover, ENaC activity did not affect the initiation, sustention, or termination of the phasic bursting generated in an intrinsic manner without synaptic inputs.

Off-diagonal matrix elements of local operators in many-body quantum systems.

In the time evolution of isolated quantum systems out of equilibrium, local observables generally relax to a long-time asymptotic value, governed by the expectation values (diagonal matrix elements) of the corresponding operator in the eigenstates of the system. The temporal fluctuations around this value, response to further perturbations, and the relaxation toward this asymptotic value are all determined by the off-diagonal matrix elements. Motivated by this nonequilibrium role, we present generic statistical properties of off-diagonal matrix elements of local observables in two families of interacting many-body systems with local interactions. Since integrability (or lack thereof) is an important ingredient in the relaxation process, we analyze models that can be continuously tuned to integrability. We show that, for generic nonintegrable systems, the distribution of off-diagonal matrix elements is a Gaussian centered at zero. As one approaches integrability, the peak around zero becomes sharper, so the distribution is approximately a combination of two Gaussians. We characterize the proximity to integrability through the deviation of this distribution from a Gaussian shape. We also determine the scaling dependence on system size of the average magnitude of off-diagonal matrix elements.

Finite-size scaling of eigenstate thermalization.

According to the eigenstate thermalization hypothesis (ETH), even isolated quantum systems can thermalize because the eigenstate-to-eigenstate fluctuations of typical observables vanish in the limit of large systems. Of course, isolated systems are by nature finite and the main way of computing such quantities is through numerical evaluation for finite-size systems. Therefore, the finite-size scaling of the fluctuations of eigenstate expectation values is a central aspect of the ETH. In this work, we present numerical evidence that for generic nonintegrable systems these fluctuations scale with a universal power law D-1/2 with the dimension D of the Hilbert space. We provide heuristic arguments, in the same spirit as the ETH, to explain this universal result. Our results are based on the analysis of three families of models and several observables for each model. Each family includes integrable members and we show how the system size where the universal power law becomes visible is affected by the proximity to integrability.

Quantum quenches and work distributions in ultralow-density systems.

We present results on quantum quenches in lattice systems with a fixed number of particles in a much larger number of sites. Both local and global quenches in this limit generically have power-law work distributions ("edge singularities"). We show that this regime allows for large edge singularity exponents beyond that allowed by the constraints of the usual thermodynamic limit. This large-exponent singularity has observable consequences in the time evolution, leading to a distinct intermediate power-law regime in time. We demonstrate these results first using local quantum quenches in a low-density Kondo-like system, and additionally through global and local quenches in Bose-Hubbard, Aubry-Andre, and hard-core boson systems at low densities.