Statistical Mechanics
Classical simulability of noisy boson sampling (1809.01953v2)
Jelmer Renema, Valery Shchesnovich, Raul Garcia-Patron
2018-09-06
Quantum mechanics promises computational powers beyond the reach of classical computers. Current technology is on the brink of an experimental demonstration of the superior power of quantum computation compared to classical devices. For such a demonstration to be meaningful, experimental noise must not affect the computational power of the device; this occurs when a classical algorithm can use the noise to simulate the quantum system. In this work, we demonstrate an algorithm which simulates boson sampling, a quantum advantage demonstration based on many-body quantum interference of indistinguishable bosons, in the presence of optical loss. Finding the level of noise where this approximation becomes efficient lets us map out the maximum level of imperfections at which it is still possible to demonstrate a quantum advantage. We show that current photonic technology falls short of this benchmark. These results call into question the suitability of boson sampling as a quantum advantage demonstration.
Time-averaged height distribution of the Kardar-Parisi-Zhang interface (1902.08110v2)
Naftali R. Smith, Baruch Meerson, Arkady Vilenkin
2019-02-21
We study the complete probability distribution
of the time-averaged height
at point
of an evolving 1+1 dimensional Kardar-Parisi-Zhang (KPZ) interface
. We focus on short times and flat initial condition and employ the optimal fluctuation method to determine the variance and the third cumulant of the distribution, as well as the asymmetric stretched-exponential tails. The tails scale as
and
, similarly to the previously determined tails of the one-point KPZ height statistics at specified time
. The optimal interface histories, dominating these tails, are markedly different. Remarkably, the optimal history,
, of the interface height at
Bacterial range expansions on a growing front: Roughness, Fixation, and Directed Percolation (1901.07956v2)
Jordan M. Horowitz, Mehran Kardar
2019-01-23
Directed Percolation (DP) is a classic model for nonequilibrium phase transitions into a single absorbing state (fixation). It has been extensively studied by analytical and numerical techniques in diverse contexts. Recently, DP has appeared as a generic model for the evolutionary/ecological dynamics of competing bacterial populations. Range expansion -- the stochastic reproduction of bacteria competing for space to be occupied by their progeny -- leads to a fluctuating and rough growth front, which is known from experiment and simulation to affect the underlying critical behavior of the DP transition. In this work, we employ symmetry arguments to construct a pair of non-linear stochastic partial differential equations describing the co-evolution of surface roughness with the composition field of DP. Macroscopic manifestations (phenomenology) of these equations on growth patterns and genealogical tracks of range expansion are discussed; followed by a renormalization group analysis of possible scaling behaviors at the DP transition.
Effect of a magnetic field on the thermodynamic uncertainty relation (1903.06480v2)
Hyun-Myung Chun, Lukas P. Fischer, Udo Seifert
2019-03-15
The thermodynamic uncertainty relation provides a universal lower bound on the product of entropy production and the fluctuations of any current. While proven for Markov dynamics on a discrete set of states and for overdamped Langevin dynamics, its status for underdamped dynamics is still open. We consider a two-dimensional harmonically confined charged particle in a magnetic field under the action of an external torque. We show analytically that, depending on the sign of the magnetic field, the thermodynamic uncertainty relation does not hold for the currents associated with work and heat. A strong magnetic field can effectively localize the particle with concomitant bounded fluctuations and low dissipation. Numerical results for a three-dimensional variant and for further currents suggest that the existence of such a bound depends crucially on the specific current.
Conducting transition analysis of thin films composed of long flexible macromolecules: Percolation study (1609.02064v7)
Yuki Norizoe, Hiroshi Morita
2015-12-11
Simulating percolation and critical phenomena of labelled species inside films composed of single-component linear homogeneous macromolecules using molecular Monte Carlo method in 3 dimensions, we study dependence of these conducting transition and critical phenomena upon both thermal movement, i.e. spontaneous mobility, and extra-molecular topological constraints of the molecules. Systems containing topological constraints and/or composed of immobile particles, e.g. lattice models and chemical gelation, were studied in conventional works on percolation. Coordinates of the randomly distributed particles in the conventional lattice models are limited to discrete lattice points. Moreover, each particle is spatially fixed at the distributed position, which results in a temporally unchanged network structure. Although each polymer in the chemical gels can spontaneously move in the continuous space, the network structure is fixed when cross-linking reaction ends. By contrast to these conventional systems, all the molecules in the present system freely move and spontaneously diffuse in the continuous space. The network structure of the present molecules continues changing dynamically. The percolation and critical phenomena of such dynamic network structures are examined here. We reveal that these phenomena also occur in the present system, and that both the universality class and percolation threshold are independent from the extra-molecular topological constraints.
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