Stochastic process behind nonlinear thermodynamic quantum master equation

We propose a piecewise deterministic Markovian jump process in Hilbert space such that the covariance matrix of this stochastic process solves the thermodynamic quantum master equation. The proposed stochastic process is particularly simple because the normalization of the vectors in Hilbert space is preserved only on average. As a consequence of the nonlinearity of the thermodynamic master equation, the construction of stochastic trajectories involves the density matrix as a running ensemble average. We identify a principle of detailed balance and a fluctuation-dissipation relation for our Markovian jump process.Comment: 4 page

Cryptochromes and neuronal-activity markers colocalize in the retina of migratory birds during magnetic orientation

Migratory birds can use a magnetic compass for orientation during their migratory journeys covering thousands of kilometers. But how do they sense the reference direction provided by the Earth’s magnetic field? Behavioral evidence and theoretical considerations have suggested that radical-pair processes in differently oriented, light-sensitive molecules of the retina could enable migratory birds to perceive the magnetic field as visual patterns. The cryptochromes (CRYs) have been suggested as the most likely candidate class of molecules, but do CRYs exist in the retina of migratory birds? Here, we show that at least one CRY1 and one CRY2 exist in the retina of migratory garden warblers and that garden-warbler CRY1 (gwCRY1) is cytosolic. We also show that gwCRY1 is concentrated in specific cells, particularly in ganglion cells and in large displaced ganglion cells, which also showed high levels of neuronal activity at night, when our garden warblers performed magnetic orientation. In addition, there seem to be striking differences in CRY1 expression between migratory and nonmigratory songbirds at night. The difference in CRY1 expression between migrants and nonmigrants is particularly pronounced in the large displaced ganglion cells known to project exclusively to a brain area where magnetically sensitive neurons have been reported. Consequently, cytosolic gwCRY1 is well placed to possibly be the primary magnetic-sensory molecule required for light-mediated magnetoreception

Localisation of the putative magnetoreceptive protein Cryptochrome 1b in the retinae of migratory birds and homing pigeons

Cryptochromes are ubiquitously expressed in various animal tissues including the retina. Some cryptochromes are involved in regulating circadian activity. Cryptochrome proteins have also been suggested to mediate the primary mechanism in light-dependent magnetic compass orientation in birds. Cryptochrome 1b (Cry1b) exhibits a unique carboxy terminus exclusively found in birds so far, which might be indicative for a specialised function. Cryptochrome 1a (Cry1a) is so far the only cryptochrome protein that has been localised to specific cell types within the retina of migratory birds. Here we show that Cry1b, an alternative splice variant of Cry1a, is also expressed in the retina of migratory birds, but it is primarily located in other cell types than Cry1a. This could suggest different functions for the two splice products. Using diagnostic bird-specific antibodies (that allow for a precise discrimination between both proteins), we show that Cry1b protein is found in the retinae of migratory European robins (Erithacus rubecula), migratory Northern Wheatears (Oenanthe oenanthe) and pigeons (Columba livia). In all three species, retinal Cry1b is localised in cell types which have been discussed as potentially well suited locations for magnetoreception: Cry1b is observed in the cytosol of ganglion cells, displaced ganglion cells, and in photoreceptor inner segments. The cytosolic rather than nucleic location of Cry1b in the retina reported here speaks against a circadian clock regulatory function of Cry1b and it allows for the possible involvement of Cry1b in a radical-pair-based magnetoreception mechanism

Fluctuation-Induced Interactions between Rods on a Membrane

We consider the interaction between two rods embedded in a fluctuating surface. The modification of fluctuations by the rods leads to an attractive long-range interaction between them. We consider fluctuations governed by either surface tension (films) or bending rigidity (membranes). In both cases the interaction falls off with the separation of the rods as $1/R^4$. The orientational part of the interaction is proportional to $\cos^2\left[ \theta_1+\theta_2 \right]$ in the former case, and to $\cos^2\left[ 2\left(\theta_1+\theta_2\right) \right]$ in the latter, where $\theta_1$ and $\theta_2$ are angles between the rods and the line joining them. These interactions are somewhat reminiscent of dipolar forces and will tend to align collections of such rods into chains.Comment: REVTEX, 14 pages, with 2 Postscript figure

Critical dynamics of an isothermal compressible non-ideal fluid

A pure fluid at its critical point shows a dramatic slow-down in its dynamics, due to a divergence of the order-parameter susceptibility and the coefficient of heat transport. Under isothermal conditions, however, sound waves provide the only possible relaxation mechanism for order-parameter fluctuations. Here we study the critical dynamics of an isothermal, compressible non-ideal fluid via scaling arguments and computer simulations of the corresponding fluctuating hydrodynamics equations. We show that, below a critical dimension of 4, the order-parameter dynamics of an isothermal fluid effectively reduces to "model A," characterized by overdamped sound waves and a divergent bulk viscosity. In contrast, the shear viscosity remains finite above two dimensions. Possible applications of the model are discussed.Comment: 19 pages, 7 figures; v3: minor corrections and clarifications; as published in Phys. Rev.

Chemical Magnetoreception: Bird Cryptochrome 1a Is Excited by Blue Light and Forms Long-Lived Radical-Pairs

Cryptochromes (Cry) have been suggested to form the basis of light-dependent magnetic compass orientation in birds. However, to function as magnetic compass sensors, the cryptochromes of migratory birds must possess a number of key biophysical characteristics. Most importantly, absorption of blue light must produce radical pairs with lifetimes longer than about a microsecond. Cryptochrome 1a (gwCry1a) and the photolyase-homology-region of Cry1 (gwCry1-PHR) from the migratory garden warbler were recombinantly expressed and purified from a baculovirus/Sf9 cell expression system. Transient absorption measurements show that these flavoproteins are indeed excited by light in the blue spectral range leading to the formation of radicals with millisecond lifetimes. These biophysical characteristics suggest that gwCry1a is ideally suited as a primary light-mediated, radical-pair-based magnetic compass receptor

Active Membrane Fluctuations Studied by Micropipet Aspiration

We present a detailed analysis of the micropipet experiments recently reported in J-B. Manneville et al., Phys. Rev. Lett. 82, 4356--4359 (1999), including a derivation of the expected behaviour of the membrane tension as a function of the areal strain in the case of an active membrane, i.e., containing a nonequilibrium noise source. We give a general expression, which takes into account the effect of active centers both directly on the membrane, and on the embedding fluid dynamics, keeping track of the coupling between the density of active centers and the membrane curvature. The data of the micropipet experiments are well reproduced by the new expressions. In particular, we show that a natural choice of the parameters quantifying the strength of the active noise explains both the large amplitude of the observed effects and its remarkable insensitivity to the active-center density in the investigated range. [Submitted to Phys Rev E, 22 March 2001]Comment: 14 pages, 5 encapsulated Postscript figure

Ordering dynamics of microscopic models with nonconserved order parameter of continuous symmetry

Numerical Monte Carlo temperature-quenching experiments have been performed on two three-dimensional classical lattice models with continuous ordering symmetry: the Lebwohl-Lasher model [Phys. Rev. A 6, 426 (1972)] and the ferromagnetic isotropic Heisenberg model. Both models describe a transition from a disordered phase to an orientationally ordered phase of continuous symmetry. The Lebwohl-Lasher model accounts for the orientational ordering properties of the nematic-isotropic transition in liquid crystals and the Heisenberg model for the ferromagnetic-paramagnetic transition in magnetic crystals. For both models, which have a nonconserved order parameter, it is found that the linear scale, R(t), of the evolving order, following quenches to below the transition temperature, grows at late times in an effectively algebraic fashion, R(t)∼tn, with exponent values which are strongly temperature dependent and furthermore vary for different measures of the time-dependent length scale. The results are discussed in relation to modern theories of ordering dynamics in systems with continuous order-parameter symmetry

The `Friction' of Vacuum, and other Fluctuation-Induced Forces

The static Casimir effect describes an attractive force between two conducting plates, due to quantum fluctuations of the electromagnetic (EM) field in the intervening space. {\it Thermal fluctuations} of correlated fluids (such as critical mixtures, super-fluids, liquid crystals, or electrolytes) are also modified by the boundaries, resulting in finite-size corrections at criticality, and additional forces that effect wetting and layering phenomena. Modified fluctuations of the EM field can also account for the `van der Waals' interaction between conducting spheres, and have analogs in the fluctuation--induced interactions between inclusions on a membrane. We employ a path integral formalism to study these phenomena for boundaries of arbitrary shape. This allows us to examine the many unexpected phenomena of the dynamic Casimir effect due to moving boundaries. With the inclusion of quantum fluctuations, the EM vacuum behaves essentially as a complex fluid, and modifies the motion of objects through it. In particular, from the mechanical response function of the EM vacuum, we extract a plethora of interesting results, the most notable being: (i) The effective mass of a plate depends on its shape, and becomes anisotropic. (ii) There is dissipation and damping of the motion, again dependent upon shape and direction of motion, due to emission of photons. (iii) There is a continuous spectrum of resonant cavity modes that can be excited by the motion of the (neutral) boundaries.Comment: RevTex, 2 ps figures included. The presentation is completely revised, and new sections are adde