Separation device

A newly proposed separation devices has come out (http://physics.aps.org/articles/v5/6).

Rubí and Peter Hänggi of the University of Augsburg, Germany, led a team that has developed a new approach to these ratchet sorters. They start with a mathematical framework in which the entropy of the system is treated like potential energy, with entropy “barriers” that repel particles. These are regions where particles are restricted to a small space, which reduces the number of states (locations and velocities) that a particle can occupy. Fewer states means lower entropy. Like balls rolling down a hill, particles tend to move away from these low entropy spots.

The team applies this formalism to a tube with walls that periodically ramp from a narrow diameter to a wide diameter and back, with an asymmetric or “sawtooth” profile. This shape forms distinct but still connected chambers, or segments, each of which is a few microns long. Entropic barriers inhibit travel between segments; however, the barriers are steeper going to the left, so the net motion of the particles is to the right.

In order to clearly see the entropic effect in their computer simulation and analytical calculations, the researchers apply an oscillating force that essentially shakes the particles back and forth inside the tube. In a real experiment, this force could be an oscillating electric field.

Vitrification vs. Crystalization

The most basic difference between the glass forming (vitrification) process and the crystallization may be seen in the figure on the left. Vitrification is actually not really a transition , because it does not involve any genuinely singular behaviors, in contrast with crystallization. A very likely implication is that, vitrification should not be due to a critical mode that features long-range correlations. Its dynamics should be essentially local, like what happens to a traffic congestion.

thermodynamic zeroth law

I like this brief synopsis: (some simple concepts: intensive and extensive variables)

A system in equilibrium is characterized by a few intensive parameters such as temperature and chemical potential. The zeroth law of thermodynamics implies that when two systems can exchange a conserved, extensive property (e.g., molecules), their intensive parameters (e.g., the chemical potentials) must eventually equalize.

Do such parameters exist for far-from-equilibrium systems? We know that intensive thermodynamic parameters can be defined for nonequilibrium stationary states in systems with short-range spatial correlations. To test whether this is possible in the presence of long-range correlations, often found in such stationary states, Punyabrata Pradhan and colleagues at the University of Stuttgart, Germany, writing in Physical Review E, analyze the driven lattice gas (DLG), a favorite “toy model” of nonequilibrium statistical mechanics, in which particles with short-range interactions hop around on a lattice.

Suppose a DLG, characterized by its size, interparticle interactions, and bias, is placed in contact with an equilibrium lattice gas. Eventually the particle densities of the two gases attain two different stationary values. Consider a second DLG, with different properties, that “equilibrates” via contact with a copy of the equilibrium lattice gas used in the first experiment. If stationary contact between the two systems can indeed be characterized by an intensive variable, we should expect no change in the respective particle densities of the two DLGs while in contact. Using Monte Carlo simulations, the authors verify that the densities, upon contact, indeed remain nearly unchanged, but that there are deviations from the zeroth law, which can be largely understood in terms of an excess chemical potential associated with the contact region. – Ron Dickman

AC field driven population inversion

Non-equilibrium physics can offer much richer phenomena than equilibrium physics. One such example is the population inversion: high energy states are occupied while the low energy ones become emptied, effectively a negative temperature phenomena. It is expected that, many exotic things might be explored with this. For instance, bandwidth vanishing. A new paper reports how to achieve this using non-adiabatic switching of ac field [PRL 106, 236401 (2011)].

We show theoretically that the sudden application of an appropriate ac field to correlated lattice fermions flips the band structure and effectively switches the interaction from repulsive to attractive. The nonadiabatically driven system is characterized by a negative temperature with a population inversion. We
numerically demonstrate the converted interaction in an ac-driven Hubbard model with the nonequilibrium dynamical mean-field theory solved by the continuous-time quantum Monte Carlo method. Based on this, we propose an efficient ramp-up protocol for ac fields that can suppress heating, which leads to an effectively attractive Hubbard model with a temperature below the superconducting transition temperature of the equilibrium system.

Ballastic and Diffusive motions

The impacts of heat bath on a small system embedded in it are clear on macroscopic and stationary scale, but they remain a challenging subject from the microscopic and dynamic point of view. A simple example is the Brownian motion of a single particle placed in a air or other medium. The equilibrium statistical theory was forwarded by Einstein a century ago, yet what actually take place over very short periods are still under intensive study (see previous entries). Here comes a new report [Science, 332:802(2011)]:

For many years after Einstein's contributions, it was expected that the transition from ballistic to diffusive motion would be quite sharp, corresponding to an exponential decay of the particle's memory of its earlier velocity. However, about 50 years ago, hints from computer simulations and theory started to suggest a more complex scenario. In particular, hydrodynamic vortices in the liquid created by the particle's motion lead to memory effects, and the particle's velocity decays much more slowly than exponentially, exhibiting a t^−3/2 “long-time-tail” (12). Detailed analysis by Huang et al. of data like that shown in the second figure, panel B, where the ballistic-to-diffusive transition spans more than three decades in time, has now provided a thorough verification of the full, complicated hydrodynamic theory (13, 14). Although several previous experiments had observed the breakdown of the simple diffusion picture [e.g., (15)], the present studies extend into the ballistic regime.

What next? Li et al. mention the fascinating prospect of laser cooling a trapped particle to a temperature at which quantization of the energy of this mesoscopic object could be observed (16). Huang et al. suggest extending their measurements to Brownian motion in confined regions and heterogeneous media. Here, understanding the details of prediffusive motion over subnanometer distances could well be relevant to some biological processes, such as the lock-and-key mechanism of enzyme action.

Spin diffuses through interacting fermi gas

This is definitely a typical non-equilibrium problem. In their experiment, "A spin current is induced by spatially separating two spin components and observing their evolution in an external trapping potential." [Nature, 472:401(2011)] They found that, "interactions can be strong enough to reverse spin currents, with components of opposite spin reflecting off each other. Near equilibrium, we obtain the spin drag coefficient, the spin diffusivity and the spin susceptibility as a function of temperature on resonance and show that they obey universal laws at high temperatures. In the degenerate regime, the spin diffusivity approaches a value set by /m, the quantum limit of diffusion, where /m is Planck’s constant divided by 2π and m the atomic mass. For repulsive interactions, our measurements seem to exclude a metastable ferromagnetic state^{9, 10, 11}." For a review, click here.

How gels sediment

This experiment studies how gel particles move during the course of sedimentation.

"Depending on the kind of colloidal particles it contains, a gel will sediment in a matter of minutes or days. Understanding how shifts in the positions of the typically submicron sized particles affect the more macroscopic sedimentation process (and vice versa) could be helpful in designing industry-use gels. So far, however, no experiments have provided simultaneous access to these vastly different length scales.

Now, a group of scientists in France and Italy report in Physical Review Letters the use of light scattering to capture both the microscopic and macroscopic pictures of a gel collapsing under its own weight.

Giovanni Brambilla of the Université Montpellier, France, and colleagues filled a tall glass column with about 10 mm of a water-based gel. The sticky, colloidal particles in the gel slowly rearranged as the gel started to sediment, altering the specklelike pattern of laser light that the team scattered through a vertical slice of the gel. Over the course of ten days, Brambilla et al. captured this speckle pattern at various heights along the column and used an algorithm to extract such parameters as the particle relaxation rate, sedimentation velocity and density.

The team finds, at least in the slowly settling gels they studied, that both the microscopic and macroscopic dynamics mimic what is found in glassy polymers. Brambilla et al.’s data should thus provide a solid basis on which to test the theory of gels. – Jessica Thomas " [http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.106.118302]

Trends: Climate Modelling

Brad Marston [Physics, 4:20(2011)] suggests physicists think about tackling climate problems, e.g., how to model climate. He wrote, "In this article, I discuss specific advances in nonequilibrium statistical physics that have direct applications on efforts to understand and predict the climate. (For an excellent introduction to the general science of climate change, see David Archer’s Global Warming: Understanding the Forecast [3].) But first, let’s look at the sort of question a statistical description of the climate system would be expected to answer."

Engineering open quantum systems

The effects of an infinite environment on a finite physical system under interest are usually deciphered with equilibrium or non-equilibrium thermodynamics, where the central concept are temperature and entropy as well as Onsager-type relations. However, there exist more elaborate and accurate methods, which are essential in engineering and control. The pioneering work along this line is represented by Boltzman's equation and his H-theorem. In that treatment, the effects are carefully accounted in terms of scattering. In recent years, some general schemes, such as master equation approach and Langevin approach, have been developed to take care of the real time dynamics of open systems. These methods are widely used in laser design and quantum de-coherence and quantum measurement. The latter delves fundamentally in quantum computing. On the other hand, the coupling to environment may be utilized to good ends. Common sense may say that such couplings are not easily manipulated and usually detrimental to quantum control. However, this situation changes and these couplings becomes tractable and can be engineered. Look at this work [Nature, 470:486(2011)]:

The dynamics of an open quantum system S coupled to an environment E can be described by the unitary transformation , with ρ_SE the joint density matrix of the composite system S + E. Thus, the reduced density operator of the system will evolve as ρ_S = Tr_E(Uρ_SEU^†). The time evolution of the system can also be described by a completely positive Kraus map

with E_k operation elements satisfying , and initially uncorrelated system and environment³¹. If the system is decoupled from the environment, the general map (1) reduces to , with U_S the unitary time evolution operator acting only on the system.

Control of both coherent and dissipative dynamics is then achieved by finding corresponding sequences of maps (1) specified by sets of operation elements {E_k} and engineering these sequences in the laboratory. In particular, for the example of dissipative quantum-state preparation, pumping to an entangled state |ψ reduces to implementing appropriate sequences of dissipative maps. These maps are chosen to drive the system to the desired target state irrespective of its initial state. The resulting dynamics have then the pure state |ψ as the unique attractor, . In quantum optics and atomic physics, the techniques of optical pumping and laser cooling are successfully used for the dissipative preparation of quantum states, although on a single-particle level. The engineering of dissipative maps for the preparation of entangled states can be seen as a generalization of this concept of pumping and cooling in driven dissipative systems to a many-particle context. To be concrete, we focus on dissipative preparation of stabilizer states, which represent a large family of entangled states, including graph states and error-correcting codes³².

We start by outlining the concept of Kraus map engineering for the simplest non-trivial example of ‘pumping’ a system of two qubits into a Bell state. The Hilbert space of two qubits is spanned by the four Bell states defined as and . Here, |0 and |1 denote the computational basis of each qubit, and we use the short-hand notation |00 = |0₁|0₂, for example. These maximally entangled states are stabilizer states: the Bell state |Φ⁺, for instance, is said to be stabilized by the two stabilizer operators Z₁Z₂ and X₁X₂, where X and Z denote the usual Pauli matrices, as it is the only two-qubit state that is an eigenstate of eigenvalue +1 of these two commuting observables, that is, Z₁Z₂|Φ⁺ = |Φ⁺ and X₁X₂|Φ⁺ = |Φ⁺. In fact, each of the four Bell states is uniquely determined as an eigenstate with eigenvalues ±1 with respect to Z₁Z₂ and X₁X₂. The key idea of pumping is that we can achieve dissipative dynamics which pump the system into a particular Bell state, for example , by constructing two dissipative maps, under which the two qubits are irreversibly transferred from the +1 into the −1 eigenspaces of Z₁Z₂ and X₁X₂.

The dissipative maps are engineered with the aid of an ancilla ‘environment’ qubit^{25, 33} and a quantum circuit of coherent and dissipative operations. The form and decomposition of these maps into basic operations are discussed in Box 1. The pumping dynamics are determined by the probability of pumping from the +1 into the −1 stabilizer eigenspaces, which can be directly controlled by varying the parameters in the employed gate operations. For pumping with unit probability (p = 1), the two qubits reach the target Bell state—regardless of their initial state—after only one pumping cycle, that is, by a single application of each of the two maps. In contrast, when the pumping probability is small (p 1), the process can be regarded as the infinitesimal limit of the general map (1). In this case, the system dynamics under a repeated application of the pumping cycle are described by a master equation³⁴:

Here H_S is a system Hamiltonian, and c_k are Lindblad operators reflecting the system–environment coupling. For the purely dissipative maps discussed here, H_S = 0. Quantum jumps from the +1 into the −1 eigenspace of Z₁Z₂ and X₁X₂ are mediated by a set of two-qubit Lindblad operators (see Box 1 for details); here the system reaches the target Bell state asymptotically after many pumping cycles.

Mpemba Effect

Water is just mundane and seems well-understood in many respects. However, there are still quite a lot of things that motivate people to find more. For example, how water molecules arrange themselves when they adsorbed on an adsorbate. Another instance is, I think more associated with the thermodynamics of water: it has been claimed that, hot water cools faster than cold water when they are placed in the same chamber. This was named after its discoverer, a middle school student Mpemba. There came a latest study on this [http://arxiv.org/ftp/arxiv/papers/1101/1101.2684.pdf]:

In this paper we have presented data confirming that water initially at higher temperature cools at a faster rate than water initially at a lower temperature and that this trend continues past the point at which the two samples reach the same temperature: the crossover temperature. Furthermore, our data indicates that the starting temperature affects the crossover temperature in a reproducible manner. We have confirmed that warmer water indeed cools faster than colder water and that, surprisingly, this trend continues past the point where the temperatures of the two samples are the same. Our results show that when using optimal initial temperature conditions, the crossover temperature is found to be 2.7 oC whereas our other set of initial conditions gave a crossover temperature of -0.07 oC. These data taken together provide a definite quantitative evidence of the Mpemba effect.

quantum entanglement observable at high temperatures

Suppose there is a bulk system at thermodynamic equilibrium. Now push it away from this equilibrium states to non-equilibrium one. Due to the second law of thermodynamics, it is expected this system shall after some time relax to equilibrium eventually. This time is called the relaxation time, which serves a time scale to judge the importance of pure mechanical dynamics. Now if the latter occurs at a much shorter time than the relaxation time, it is hoped that the thermal noises will not take big role, which means the behavior is governed by the pure dynamics. This being so, a system even very high temperatures can show quantum phenomena on the short time scale. This idea was recently written in PRL [Phys. Rev. Lett. 105, 180501 (2010)]. A review is as follows [Nature, 468:769]:

The basic intuition behind this result is as follows. When a system is not in thermal equilibrium, the temperature no longer provides the relevant energy scale against which to compare the system's quantum behaviour. What matters instead is an effective temperature, which can be much lower than the absolute one. This effective temperature is obtained by multiplying the absolute temperature by the rate at which the system approaches equilibrium divided by the driving frequency, the frequency of the signal with which the system is made to oscillate. Galve and colleagues demonstrate that this new condition for entanglement — that the interaction between subsystems should be compared with the thermal energy at the effective temperature — holds quite generally and is intuitively pleasing. It says that if we can drive the system to oscillate within a shorter timescale than the time it takes to reach thermal equilibrium, then an entangled steady state can be attained at higher temperatures than the absolute one.

Does noise entail decoherence ?

Every system is in contact with its surroundings and is thus an open system. It is not possible to have exact information about its surroundings, implying a statistical treatment of the interactions between the system and its surrounding. In equilibrium thermodynamics, a statistical weight can be assigned to effect the surrounding. However, in non-equilibrium cases, where dynamics are crucial, noises of certain type are supposed to capture the physics. Usually, white noises, which are the noises from, let's say, a heat bath, cause de-coherence of quantum states. How about 1/f noises ? This kind of noise is pointing and may not be so detrimental. In this piece of work, the authors theoretically examined the fate of a quantum critical state under such 1/f noise. They found that, the criticality can be preserved. To investigate the nature of a system, one may either look at its ground state (by considering static response to certain stimuli) or its excited states (by inspecting its dynamic response to certain stimuli) or both. Basically, these methods should be the same: from G-state one could have some idea (just some idea based on clever guess) what the E-states might be and vice-versa. In many cases, the G-state is preferred, because once the G-state is known, it shows at least how to construct low energy excitations (again, vice versa). In this work, they of course have to study the excitations, since it is a non-equilibrium system. [NATURE PHYSICS, VOL 6, OCTOBER 2010 ,www.nature.com/naturephysics]

Quantum critical points are characterized by scale-invariant correlations and therefore by long-range entanglement. As such, they present fascinating examples of quantum states of matter and their study is an important theme in modern physics.
However, little is known about the fate of quantum criticality under non-equilibrium conditions. Here we investigate the effect of external noise sources on quantum critical points. It is natural to expect that noise will have a similar effect to
finite temperature, that is, destroying the subtle correlations underlying the quantum critical behaviour. Surprisingly, we find that the ubiquitous 1=f noise does preserve the critical correlations. The emergent states show an intriguing interplay of
intrinsic quantum critical and external-noise-driven fluctuations.We illustrate this general phenomenon with specific examples describing solid-state and ultracold-atoms systems. Moreover, our approach shows that genuine quantum phase transitions can exist even under non-equilibrium conditions.