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In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath couplings that is applicable even in the thermodynamic limit. We identify conditions under which thermalization happens and discuss the underlying physics. Based on these results, we also present a fully general quantum algorithm for preparing Gibbs states on a quantum computer with a certified runtime and error bound. This complements quantum Metropolis algorithms, which are expected to be efficient but have no known runtime estimates and only work for local Hamiltonians.
A Bose-Hubbard model on a dynamical lattice was introduced in previous work as a spin system analogue of emergent geometry and gravity. Graphs with regions of high connectivity in the lattice were identified as candidate analogues of spacetime geometries that contain trapped surfaces. We carry out a detailed study of these systems and show explicitly that the highly connected subgraphs trap matter. We do this by solving the model in the limit of no back-reaction of the matter on the lattice, and for states with certain symmetries that are natural for our problem. We find that in this case the problem reduces to a one-dimensional Hubbard model on a lattice with variable vertex degree and multiple edges between the same two vertices. In addition, we obtain a (discrete) differential equation for the evolution of the probability density of particles which is closed in the classical regime. This is a wave equation in which the vertex degree is related to the local speed of propagation of probability. This allows an interpretation of the probability density of particles similar to that in analogue gravity systems: matter inside this analogue system sees a curved spacetime. We verify our analytic results by numerical simulations. Finally, we analyze the dependence of localization on a gradual, rather than abrupt, falloff of the vertex degree on the boundary of the highly connected region and find that matter is localized in and around that region.
We study phase synchronization in a network motif with a starlike structure in which the central node's (the hub's) frequency is strongly detuned against the other peripheral nodes. We find numerically and experimentally a regime of remote synchronization (RS), where the peripheral nodes form a phase synchronized cluster, while the hub remains free with its own dynamics and serves just as a transmitter for the other nodes. We explain the mechanism for this RS by the existence of a free amplitude and also show that systems with a fixed or constant amplitude, such as the classic Kuramoto phase oscillator, are not able to generate this phenomenon. Further, we derive an analytic expression which supports our explanation of the mechanism.
On 27 February 2010 the M-w 8.8 Maule earthquake in Central Chile ruptured a seismic gap where significant strain had accumulated since 1835. Shortly after the mainshock a dense network of temporary seismic stations was installed along the whole rupture zone in order to capture the aftershock activity. Here, we present the aftershock distribution and first motion polarity focal mechanisms based on automatic detection algorithms and picking engines. By processing the seismic data between 15 March and 30 September 2010 from stations from IRIS, IPGP, GFZ and University of Liverpool we determined 20,205 hypocentres with magnitudes M-w between 1 and 5.5. Seismic activity occurs in six groups: 1.) Normal faulting outer rise events 2.) A shallow group of plate interface seismicity apparent at 25-35 km depth and 50-120 km distance to the trench with some variations between profiles. Along strike, the aftershocks occur largely within the zone of coseismic slip but extend similar to 50 km further north, and with predominantly shallowly dipping thrust mechanisms. Along dip, the events are either within the zone of coseismic slip, or downdip from it, depending on the coseismic slip model used. 3.) A third band of seismicity is observed further downdip at 40-50 km depth and further inland at 150-160 km trench perpendicular distance, with mostly shallow dipping (similar to 28 degrees) thrust focal mechanisms indicating rupture of the plate interface significantly downdip of the coseismic rupture, and presumably above the intersection of the continental Moho with the plate interface. 4.) A deep group of intermediate depth events between 80 and 120 km depth is present north of 36 degrees S. Within the Maule segment, a large portion of events during the inter-seismic phase originated from this depth range. 5.) The magmatic arc exhibits a small amount of crustal seismicity but does not appear to show significantly enhanced activity after the M-w 8.8 Maule 2010 earthquake. 6.) Pronounced crustal aftershock activity with mainly normal faulting mechanisms is found in the region of Pichilemu (similar to 34.5 degrees S). These crustal events occur in a similar to 30 km wide region with sharp inclined boundaries and oriented oblique to the trench. The best-located events describe a plane dipping to the southwest, consistent with one of the focal planes of the large normal-faulting aftershock (M-w = 6.9) on 11 March 2010.
Contemporary cosmological conceptions suggest that the dark matter in haloes of galaxies and galaxy clusters has most likely a clumpy structure. If a stream of gas penetrates through it, a small-scale gravitational field created by the clumps disturbs the flow resulting in momentum exchange between the stream and the dark matter. In this article, we perform an analysis of this effect, based on the hierarchical halo model of the dark matter structure and Navarro-Frenk-White density profiles. We consider the clumps of various masses, from the smallest up to the highest ones M = 10(9) M circle dot. It has been found that in any event the effect grows with the mass of the clump: not only the drag force F acting on the clump but also its acceleration w = F/M increases.
We discuss various astrophysical systems. The mechanism proved to be ineffective in the case of galaxy or galaxy cluster collisions. On the other hand, it played an important role during the process of galaxy formation. As a result, the dark matter should have formed a more compact, oblate and faster rotating substructure in the halo of our Galaxy. We have shown that this thick disc should be more clumpy than the halo. This fact is very important for the indirect detection experiments since it is the clumps that give the main contribution to the annihilation signal. Our calculations show that the mechanism of momentum exchange between the dark and baryon matter is ineffective on the outskirts of the galactic halo. It means that the clumps from there were not transported to the thick disc, and this region should be more clumpy than the halo on the average.
To explore the ionization conditions in highly-ionized absorbers at high redshift, we study in detail two intervening O vi absorbers at z approximate to 2 toward the quasar PKS 1448-232, based on high (R approximate to 75 000) and intermediate (R approximate to 45 000) resolution optical VLT/UVES spectra. We find that both absorption systems are composed of several narrow subcomponents with typical Civ/O VI Doppler-parameters of b < 10 km s(-1). This implies that the gas temperatures are T < 10(5) K and that the absorbers are photoionized by the UV background. The system at z = 2.1098 represents a simple, isolated O VI absorber that has only two absorption components and is relatively metal-rich (Z similar to 0.6 solar). Ioinization modeling implies that the system is photoionized with O VI, C IV, and H I coexisting in the same gas phase. The second system at z = 2.1660 represents a complicated, multi-component absorption system with eight O VI components spanning almost 300 km s(-1) in radial velocity. The photoionization modeling implies that the metallicity is non-uniform and relatively low (<= 0.1 solar) and that the O VI absorption must arise in a gas phase that differs from that traced by C IV, C III, and H I. Our detailed study of the two O VI systems towards PKS 1448-232 shows that multi-phase, multi-component high-ion absorbers similar to the one at z = 2.1660 can be described by applying a detailed ionization modeling of the various subcomponents to obtain reliable measurements of the physical conditions and the metal abundances in the gas.
Completely positive, trace preserving (CPT) maps and Lindblad master equations are both widely used to describe the dynamics of open quantum systems. The connection between these two descriptions is a classic topic in mathematical physics. One direction was solved by the now famous result due to Lindblad, Kossakowski, Gorini and Sudarshan, who gave a complete characterisation of the master equations that generate completely positive semi-groups. However, the other direction has remained open: given a CPT map, is there a Lindblad master equation that generates it (and if so, can we find its form)? This is sometimes known as the Markovianity problem. Physically, it is asking how one can deduce underlying physical processes from experimental observations.
We give a complexity theoretic answer to this problem: it is NP-hard. We also give an explicit algorithm that reduces the problem to integer semi-definite programming, a well-known NP problem. Together, these results imply that resolving the question of which CPT maps can be generated by master equations is tantamount to solving P = NP: any efficiently computable criterion for Markovianity would imply P = NP; whereas a proof that P = NP would imply that our algorithm already gives an efficiently computable criterion. Thus, unless P does equal NP, there cannot exist any simple criterion for determining when a CPT map has a master equation description.
However, we also show that if the system dimension is fixed (relevant for current quantum process tomography experiments), then our algorithm scales efficiently in the required precision, allowing an underlying Lindblad master equation to be determined efficiently from even a single snapshot in this case.
Our work also leads to similar complexity-theoretic answers to a related long-standing open problem in probability theory.
If a one-dimensional quantum lattice system is subject to one step of a reversible discrete-time dynamics, it is intuitive that as much "quantum information" as moves into any given block of cells from the left, has to exit that block to the right. For two types of such systems - namely quantum walks and cellular automata - we make this intuition precise by defining an index, a quantity that measures the "net flow of quantum information" through the system. The index supplies a complete characterization of two properties of the discrete dynamics. First, two systems S-1, S-2 can be "pieced together", in the sense that there is a system S which acts like S-1 in one region and like S-2 in some other region, if and only if S-1 and S-2 have the same index. Second, the index labels connected components of such systems: equality of the index is necessary and sufficient for the existence of a continuous deformation of S-1 into S-2. In the case of quantum walks, the index is integer-valued, whereas for cellular automata, it takes values in the group of positive rationals. In both cases, the map S bar right arrow. ind S is a group homomorphism if composition of the discrete dynamics is taken as the group law of the quantum systems. Systems with trivial index are precisely those which can be realized by partitioned unitaries, and the prototypes of systems with non-trivial index are shifts.
We propose a simple theoretical model for aggregative and fragmentative collisions in Saturn's dense rings. In this model the ring matter consists of a bimodal size distribution: large (meter sized) boulders and a population of smaller particles (tens of centimeters down to dust). The small particles can adhesively stick to the boulders and can be released as debris in binary collisions of their carriers. To quantify the adhesion force we use the JKR theory (Johnson, K., Kendall, K., Roberts, A. [1971]. Proc. R. Soc. Lond. A 324, 301-313). The rates of release and adsorption of particles are calculated, depending on material parameters, sizes, and plausible velocity dispersions of carriers and debris particles. In steady state we obtain an expression for the amount of free debris relative to the fraction still attached to the carriers. In terms of this conceptually simple model a paucity of subcentimeter particles in Saturn's rings (French, R.G., Nicholson, P.D. [2000]. Icarus 145, 502-523; Marouf, E. et al. [2008]. Abstracts for "Saturn after Cassini-Huygens" Symposium, Imperial College London, UK, July 28 to August 1, p. 113) can be understood as a consequence of the increasing strength of adhesion (relative to inertial forces) for decreasing particle size. In this case particles smaller than a certain critical radius remain tightly attached to the surfaces of larger boulders, even when the boulders collide at their typical speed. Furthermore, we find that already a mildly increased velocity dispersion of the carrier-particles may significantly enhance the fraction of free debris particles, in this way increasing the optical depth of the system.
We consider the mean first-passage time of a random walker moving in a potential landscape on a finite interval, the starting and end points being at different potentials. From analytical calculations and Monte Carlo simulations we demonstrate that the mean first-passage time for a piecewise linear curve between these two points is minimized by the introduction of a potential barrier. Due to thermal fluctuations, this barrier may be crossed. It turns out that the corresponding expense for this activation is less severe than the gain from an increased slope towards the end point. In particular, the resulting mean first-passage time is shorter than for a linear potential drop between the two points.