Quantum sine-Gordon dynamics on analogue curved spacetime in a weakly imperfect scalar Bose gas

Using the coherent state functional integral expression of the partition function, we show that the sine-Gordon model on an analogue curved spacetime arises as the effective quantum field theory for phase fluctuations of a weakly imperfect Bose gas on an incompressible background superfluid flow when these fluctuations are restricted to a subspace of the single-particle Hilbert space. We consider bipartitions of the single-particle Hilbert space relevant to experiments on ultracold bosonic atomic or molecular gases, including, e.g., restriction to high- or low-energy sectors of the dynamics and spatial bipartition corresponding to tunnel-coupled planar Bose gases. By assuming full unitary quantum control in the low-energy subspace of a trapped gas, we show that (1) appropriately tuning the particle number statistics of the lowest-energy mode partially decouples the low- and high-energy sectors, allowing any low-energy single-particle wave function to define a background for sine-Gordon dynamics on curved spacetime and (2) macroscopic occupation of a quantum superposition of two states of the lowest two modes produces an analogue curved spacetime depending on two background flows, with respective weights continuously dependent on the corresponding weights of the superposed quantum states.Comment: 12 pages, 1 figur

Amplification of the quantum superposition macroscopicity of a flux qubit by a magnetized Bose gas

We calculate a measure of superposition macroscopicity $\mathcal{M}$ for a superposition of screening current states in a superconducting flux qubit (SFQ), by relating $\mathcal{M}$ to the action of an instanton trajectory connecting the potential wells of the flux qubit. When a magnetized Bose-Einstein condensed (BEC) gas containing $N_{B}\sim \mathcal{O}(10^6)$ atoms is brought into a $\mathcal{O}(1)$ $\mu\text{m}$ proximity of the flux qubit in an experimentally realistic geometry, we demonstrate the appearance of a two- to five-fold amplification of $\mathcal{M}$ over the bare value without the BEC, by calculating the instantion trajectory action from the microscopically derived effective flux Lagrangian of a hybrid quantum system composed of the flux qubit and a spin-$F$ atomic Bose gas. Exploiting the connection between $\mathcal M$ and the maximal metrological usefulness of a multimode superposition state, we show that amplification of $\mathcal{M}$ in the ground state of the hybrid system is equivalent to a decrease in the quantum Cram\'{e}r-Rao bound for estimation of an externally applied flux. Our result therefore demonstrates the increased usefulness of the BEC--SFQ hybrid system as a sensor of ultraweak magnetic fields below the standard quantum limit.Comment: 10 pages, 2 figure

Domain formation in membranes with quenched protein obstacles: Lateral heterogeneity and the connection to universality classes

We show that lateral fluidity in membranes containing quenched protein obstacles belongs to the universality class of the two-dimensional random-field Ising model. The main feature of this class is the absence of a phase transition: there is no critical point, and macroscopic domain formation does not occur. Instead, there is only one phase. This phase is highly heterogeneous, with a structure consisting of micro-domains. The presence of quenched protein obstacles thus provides a mechanism to stabilize lipid rafts in equilibrium. Crucial for two-dimensional random-field Ising universality is that the obstacles are randomly distributed, and have a preferred affinity to one of the lipid species. When these conditions are not met, standard Ising or diluted Ising universality apply. In these cases, a critical point does exist, marking the onset toward macroscopic demixing.Comment: 10 pages, 10 figure

Red blood cells and other non-spherical capsules in shear flow: oscillatory dynamics and the tank-treading-to-tumbling transition

We consider the motion of red blood cells and other non-spherical microcapsules dilutely suspended in a simple shear flow. Our analysis indicates that depending on the viscosity, membrane elasticity, geometry and shear rate, the particle exhibits either tumbling, tank-treading of the membrane about the viscous interior with periodic oscillations of the orientation angle, or intermittent behavior in which the two modes occur alternately. For red blood cells, we compute the complete phase diagram and identify a novel tank-treading-to-tumbling transition at low shear rates. Observations of such motions coupled with our theoretical framework may provide a sensitive means of assessing capsule properties.Comment: 11 pages, 4 figure

Metastability and uniqueness of vortex states at depinning

We present results from numerical simulations of transport of vortices in the zero-field cooled (ZFC) and the field-cooled (FC) state of a type-II superconductor. In the absence of an applied current $I$, we find that the FC state has a lower defect density than the ZFC state, and is stable against thermal cycling. On the other hand, by cycling $I$, surprisingly we find that the ZFC state is the stable state. The FC state is metastable as manifested by increasing $I$ to the depinning current $I_{c}$, in which case the FC state evolves into the ZFC state. We also find that all configurations acquire a unique defect density at the depinning transition independent of the history of the initial states.Comment: 4 pages, 4 figures. Problem of page size correcte

Fluids with quenched disorder: Scaling of the free energy barrier near critical points

In the context of Monte Carlo simulations, the analysis of the probability distribution $P_L(m)$ of the order parameter $m$, as obtained in simulation boxes of finite linear extension $L$, allows for an easy estimation of the location of the critical point and the critical exponents. For Ising-like systems without quenched disorder, $P_L(m)$ becomes scale invariant at the critical point, where it assumes a characteristic bimodal shape featuring two overlapping peaks. In particular, the ratio between the value of $P_L(m)$ at the peaks ($P_{L, max}$) and the value at the minimum in-between ($P_{L, min}$) becomes $L$-independent at criticality. However, for Ising-like systems with quenched random fields, we argue that instead $\Delta F_L := \ln (P_{L, max} / P_{L, min}) \propto L^\theta$ should be observed, where $\theta>0$ is the "violation of hyperscaling" exponent. Since $\theta$ is substantially non-zero, the scaling of $\Delta F_L$ with system size should be easily detectable in simulations. For two fluid models with quenched disorder, $\Delta F_L$ versus $L$ was measured, and the expected scaling was confirmed. This provides further evidence that fluids with quenched disorder belong to the universality class of the random-field Ising model.Comment: sent to J. Phys. Cond. Mat