Exact relaxation in a class of non-equilibrium quantum lattice systems

A reasonable physical intuition in the study of interacting quantum systems says that, independent of the initial state, the system will tend to equilibrate. In this work we study a setting where relaxation to a steady state is exact, namely for the Bose-Hubbard model where the system is quenched from a Mott quantum phase to the strong superfluid regime. We find that the evolving state locally relaxes to a steady state with maximum entropy constrained by second moments, maximizing the entanglement, to a state which is different from the thermal state of the new Hamiltonian. Remarkably, in the infinite system limit this relaxation is true for all large times, and no time average is necessary. For large but finite system size we give a time interval for which the system locally "looks relaxed" up to a prescribed error. Our argument includes a central limit theorem for harmonic systems and exploits the finite speed of sound. Additionally, we show that for all periodic initial configurations, reminiscent of charge density waves, the system relaxes locally. We sketch experimentally accessible signatures in optical lattices as well as implications for the foundations of quantum statistical mechanics.Comment: 8 pages, 3 figures, replaced with final versio

State-space model identification and feedback control of unsteady aerodynamic forces

Unsteady aerodynamic models are necessary to accurately simulate forces and develop feedback controllers for wings in agile motion; however, these models are often high dimensional or incompatible with modern control techniques. Recently, reduced-order unsteady aerodynamic models have been developed for a pitching and plunging airfoil by linearizing the discretized Navier-Stokes equation with lift-force output. In this work, we extend these reduced-order models to include multiple inputs (pitch, plunge, and surge) and explicit parameterization by the pitch-axis location, inspired by Theodorsen's model. Next, we investigate the na\"{\i}ve application of system identification techniques to input--output data and the resulting pitfalls, such as unstable or inaccurate models. Finally, robust feedback controllers are constructed based on these low-dimensional state-space models for simulations of a rigid flat plate at Reynolds number 100. Various controllers are implemented for models linearized at base angles of attack $\alpha_0=0^\circ, \alpha_0=10^\circ$, and $\alpha_0=20^\circ$. The resulting control laws are able to track an aggressive reference lift trajectory while attenuating sensor noise and compensating for strong nonlinearities.Comment: 20 pages, 13 figure

Different forms of the bovine PrP gene have five or six copies of a short, G-C-rich element within the protein-coding exon

Current models of the virus-like agents of scrapie and bovine spongiform encephalopathy (BSE) have to take into account that structural changes in a host-encoded protein (PrP protein) exhibit an effect on the time course of these diseases and the survival time of any man or animal exposed to these pathogens. We report here the sequence of different forms of the bovine PrP gene which contain either five or six copies of a short, G-C-rich element which encodes the octapeptide Pro-His-Gly-Gly-Gly-Trp-Gly-Gln or its longer variants Pro-Gln/His-Gly-Gly-Gly-Gly-Trp-Gly-Gln. Out of 12 cattle, we found eight animals homozygous for genes with six copies of the Gly-rich peptide (6:6), while four were heterozygous (6:5). Two confirmed cases of BSE occurred in (6: 6) homozygous animals. Bovine spongiform encephalopathy (BSE) is a transmissible disease (Fraser et al., 1988; Dawson et al., 1990; Barlow & Middleton, 1990) which produces neuropathological lesions in cattle similar to those seen in ovine scrapie (Wells et al., 1987) and the rare human dementias Creutzfeldt-Jakob disease (CJD) and Gerstmann-Str/iussler syndrome (GSS) (Beck & Daniel, 1987). A cellular membrane protein (PrP) has a key role in the transmission and development of these diseases. This protein accumulates in the brain and other tissues during the protracted time course of these diseases and, in a disease-specific, protease-resistant isoform (SAF-PrP), has been purified by subcellular fractionation of scrapie

On non-normality and classification of amplification mechanisms in stability and resolvent analysis

We seek to quantify non-normality of the most amplified resolvent modes and predict their features based on the characteristics of the base or mean velocity profile. A 2-by-2 model linear Navier-Stokes (LNS) operator illustrates how non-normality from mean shear distributes perturbation energy in different velocity components of the forcing and response modes. The inverse of their inner product, which is unity for a purely normal mechanism, is proposed as a measure to quantify non-normality. In flows where there is downstream spatial dependence of the base/mean, mean flow advection separates the spatial support of forcing and response modes which impacts the inner product. Success of mean stability analysis depends on the normality of amplification. If the amplification is normal, the resolvent operator written in its dyadic representation reveals that the adjoint and forward stability modes are proportional to the forcing and response resolvent modes. If the amplification is non-normal, then resolvent analysis is required to understand the origin of observed flow structures. Eigenspectra and pseudospectra are used to characterize these phenomena. Two test cases are studied: low Reynolds number cylinder flow and turbulent channel flow. The first deals mainly with normal mechanisms and quantification of non-normality using the inverse inner product of the leading forcing and response modes agrees well with the product of the resolvent norm and distance between the imaginary axis and least stable eigenvalue. In turbulent channel flow, structures result from both normal and non-normal mechanisms. Mean shear is exploited most efficiently by stationary disturbances while bounds on the pseudospectra illustrate how non-normality is responsible for the most amplified disturbances at spatial wavenumbers and temporal frequencies corresponding to well-known turbulent structures

Response time to colored stimuli in the full visual field

Peripheral visual response time was measured in seven dark adapted subjects to the onset of small (45' arc diam), brief (50 msec), colored (blue, yellow, green, red) and white stimuli imaged at 72 locations within their binocular field of view. The blue, yellow, and green stimuli were matched for brightness at about 2.6 sub log 10 units above their absolute light threshold, and they appeared at an unexpected time and location. These data were obtained to provide response time and no-response data for use in various design disciplines involving instrument panel layout. The results indicated that the retina possesses relatively concentric regions within each of which mean response time can be expected to be of approximately the same duration. These regions are centered near the fovea and extend farther horizontally than vertically. Mean foveal response time was fastest for yellow and slowest for blue. Three and one-half percent of the total 56,410 trials presented resulted in no-responses. Regardless of stimulus color, the lowest percentage of no-responses occurred within 30 deg arc from the fovea and the highest within 40 deg to 80 deg arc below the fovea

Scalar meson in dynamical and partially quenched two-flavor QCD: lattice results and chiral loops

This is an exploratory study of the lightest non-singlet scalar $q\bar q$ state on the lattice with two dynamical quarks. Domain Wall fermions are used for both sea and valence quarks on a 16^3*32 lattice with an inverse lattice spacing of 1.7 GeV. We extract the scalar meson mass 1.58(34) GeV from the exponential time-dependence of the dynamical correlators with $m_{val}=m_{sea}$ and N_f=2. Since this statistical error-bar from dynamical correlators is rather large, we analyze also the partially quenched lattice correlators with $m_{val}$ not equal $m_{sea}$. They are positive for $m_{val}>=m_{sea}$ and negative for $m_{val}<m_{sea}$. In order to understand this striking effect of partial quenching, we derive the scalar correlator within the Partially Quenched ChPT and find it describes lattice correlators well. The leading unphysical contribution in Partially Quenched ChPT comes from the exchange of the two pseudoscalar fields and is also positive for $m_{val}>=m_{sea}$ and negative for $m_{val}<m_{sea}$ at large t. After the subtraction of this unphysical contribution from the partially quenched lattice correlators, the correlators are positive and exponentially falling. The resulting scalar meson mass 1.51(19) GeV from the partially quenched correlators is consistent with the dynamical result and has appreciably smaller error-bar.Comment: 23 pages, 8 figure

Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition

Dynamic mode decomposition (DMD) provides a practical means of extracting insightful dynamical information from fluids datasets. Like any data processing technique, DMD's usefulness is limited by its ability to extract real and accurate dynamical features from noise-corrupted data. Here we show analytically that DMD is biased to sensor noise, and quantify how this bias depends on the size and noise level of the data. We present three modifications to DMD that can be used to remove this bias: (i) a direct correction of the identified bias using known noise properties, (ii) combining the results of performing DMD forwards and backwards in time, and (iii) a total least-squares-inspired algorithm. We discuss the relative merits of each algorithm, and demonstrate the performance of these modifications on a range of synthetic, numerical, and experimental datasets. We further compare our modified DMD algorithms with other variants proposed in recent literature