N.B. Kopnin, G. Volovik, collaborators Victor S. L'vov (The Weizmann Institute of Science, Israel), Sergey V. Nazarenko (University of Warwick, UK)
This theoretical work is closely connected to the experimental effort in the laboratory, New class of superfluid turbulence has been recently discovered experimentally by ROTA group under conditions that the normal component is clamped in the container frame due to its high viscosity. In contrast to classical turbulence, the transition to superfluid turbulence has been found to be velocity independent. According to the experiment, a few seed vortices injected into the He-3 B superflow triggered a transition into a state with a turbulent vortex tangle for temperatures T<0.6 Tc while the same injection at higher temperatures did not create any substantial number of vortices in the final state. In these measurements, the superfluid Reynolds numbers as high as 200 have been reached without any noticeable dependence of the transition temperature on the initial superflow velocity.
The theoretical model supported by numerical simulations has been developed that explains the transition to turbulence in terms of the vortex instability governed by the mutual friction between the normal and superfluid components that appears in the presence of quantized vortices [5]. The coarse grained description of the developed superfluid turbulence was derived, which is characterized by two Reynolds parameters, one of them being independent of flow velocity [16]. The spectrum of developed turbulence was calculated. It was shown that it is modified by the nonlinear energy dissipation caused by the mutual friction between quantized vortices and the normal component of the liquid. In some region of two Reynolds parameters characterizing the flow of a superfluid, a new state of the fully developed turbulence was found. This state displays both the Kolmogorov-Obukhov scaling law E(k)~ k-5/3 and the new scaling law E(k)~ k-3 , each in a well separated range of k [7].
N.B. Kopnin, collaborators: V.M. Vinokur (Argonne National Laboratory, US), A. S. Mel'nikov (Nizhny Novgorod, Russia)
Theoretical studies of mesoscopic superconductors were concentrated on the effects of weak disorder on transport properties and energy states of Andreev wires, i.e., in normal conductors surrounded by a superconducting environment. Vorices in type II superconductors and filamentary intermediate state of type I superconductors in addition to artificially fabricated SN heterostructures can be the examples of such Andreev wires.
Like in usual conductors, the single electron transport in Andreev wires is associated with transverse modes confined in the normal region. However, in contrast to the usual conductors, the heat conductance of ballistic Andreev wire appears to be substantially lower than what can be obtained from the Wiedemann—Franz law using the normal electrical conductance of the wire due to much smaller group velocity of the Andreev modes. In disordered Andreev wires with a long mean free path, the ballistic transport changes to diffusion. In addition to the known Andreev diffusion decreasing with an increase in the mean free path, the heat conductance includes a diffusive drift along the Andreev states produced by a small particle-hole asymmetry. This drift contribution increases with increasing mean free path. The conductance thus has a minimum, which should lead to a peculiar re-entrant localization of transport as a function of the mean free path [19].
G. Volovik, collaborator Frans Klinkhamer (University of Karlsruhe, Germany)
There is a class of quantum phase transitions which occur without change of symmetry and is related to the change of the topology of the fermionic spectrum. Lifshitz transition with change of the topology of Fermi surface in metals is an example. The other types of such transitions are related to point and line nodes in the spectrum of fermions. In particular there can be quantum phase transitions that separate a vacuum state with fully-gapped fermion spectrum from a vacuum state with topologically-protected Fermi points (gap nodes). In the context of condensed-matter physics, such a quantum phase transition with Fermi point splitting may occur for a system of ultracold fermionic atoms in the region of the BEC--BCS crossover, provided Cooper pairing occurs in the non-s-wave channel. For elementary particle physics, the splitting of Fermi points may lead to CPT violation, neutrino oscillations, and other phenomena [4].
G. Volovik, collaborator Carlos Barcelo (Instituto de Astrofisica de Andalucia, Spain)
There are fundamental relations between three vast areas of physics: particle physics, cosmology and condensed matter. These relations constitute a successful example of the unity of physics. Fundamental links between cosmology and particle physics, in other words, between macro- and micro-worlds, have been well established. There is a unified system of laws governing all scales from subatomic particles to the Cosmos and this principle is widely exploited in the description of the physics of the early Universe, baryogenesis, cosmological nucleosynthesis, etc. The connection of these two fields with the third ingredient of the modern physics -- condensed matter -- is the main goal of our program. These connections allow us to simulate the least known features of high-energy physics and cosmology: the properties of the quantum vacuum.
Starting from the assumption that general relativity might be an emergent phenomenon showing up at low-energies from a condensed-matter-like underlying structure, we re-analyzed the stability of Einstein static Universe. In this scenario, it is sensible to consider a general relativistic configuration as in contact with a thermal reservoir. We calculated the free energy at a fixed temperature of an Einstein configuration filled with radiation and found that the Einstein state is actually stable under the stated condition [1]. This differs from the prediction of the fundamental general relativity: though the same local equations of general relativity were used, the global properties of the Universe appeared to be different in emergent and fundamental gravity.
The dark energy (the vacuum energy) estimated using the methods of particle physics is now in huge disagreement with modern cosmological experiments. This is the main cosmological constant problem. The condensed-matter experience gives the hint how this problem can be solved: the trans-Planckian degrees of freedom completely cancel the contribution of zero-point fluctuations to the vacuum energy due to thermodynamic idenity. The next step is to find the origin of the observed small cosmological constant L. We discussed from the condensed-matter point of view the recent idea that the Poisson fluctuations of cosmological constant about zero could be a source of the observed dark energy. We calculated the magnitude of thermodynamic fluctuations of L and found that it can be consistent with observations for the special choice of the volume of the Universe, which must be much bigger than the volume within the cosmological horizon [17].
We appplied the thermodynamic principles also for the problem of coexistence of several quantum vacua [15], [20]. We found that at the coexistence point all the vacua have zero cosmological constant. The coexistence of vacua can be regulated by the exchange of the global fermionic charges between the vacua, such as baryonic, leptonic or family charge. If the coexistence is regulated by the baryonic charge, all the coexisting vacua exhibit the baryonic asymmetry which could explain the excess of matter over antimatter in our Universe.
T. T. Heikkilä, N. Kopnin, J. Voutilainen, and P. Virtanen, in collaboration with the Pico group and F. Giazotto, F. Taddei, R. Fazio, and F. Beltram, Scuola Normale Superiore, Pisa, Italy
We have studied theoretically the nonequilibrium dynamics of superconductor-insulator-normal-metal-insulator-superconductor (SINIS) systems. Such devices can be used as efficient Peltier coolers. We have studied the ultimate limits of such cooling and the nonequilibrium electron energy distributions in these systems, including quantitatively the roles of energy relaxation [Pico13] and possible nonequilibrium induced in the superconductors. Moreover, we have studied a system which combines a SINIS cooler with a superconductor-normal-metal-superconductor Josephson weak link and shown how such a system can be used as an accurately tunable, low-dissipation supercurrent transistor with high current and power gains [2, Pico8]. Based on this theory, the first experimental operation of such a “cold electron transistor” has been demonstrated in the Pico group [Pico11].
We have also theoretically examined the thermoelectric phenomena in mesoscopic normal-metal wires in contact to superconductors [13, 14]. In such devices, recent experiments have shown that the thermopower, i.e., the voltage created by the temperature difference in the absence of charge currents, can exceed the previously known theoretical predictions by a few orders of magnitude, and moreover, it can be controlled with a magnetic flux. In our study, we have shown that the presence of supercurrent in such systems leads to the observed thermoelectric effects. Our theory is in good agreement with the experimental observations and predicts how it can be confirmed via an experiment slightly different from the previous ones.
T. T. Heikkilä, T. Ojanen and P. Virtanen, in collaboration with the Nano group and E. B. Sonin (Racah Hebrew University of Jerusalem, Israel), G. Johansson (University of Karlsruhe, Germany and Chalmers University of Technology, Gothenburg, Sweden) and F. K. Wilhelm (Ludwig-Maximilian University of Munich, Germany)
We have studied theoretically how the current fluctuations and their statistics can be measured in mesoscopic systems. We have considered the limitations of classical measurement schemes in measuring the third and higher cumulants of fluctuations [s1,Nano3]. Cyclostationary driving provides an easier access to the odd cumulants compared to DC driving. We have also considered novel mesoscopic detectors based on a small Josephson junction with a high-resistance environment, which allow for a sensitive and large-bandwidth detection of noise [Nano2,3]. Moreover, in such detectors, one can access the asymmetry of the noise, which is not possible in the standard schemes. Such a detector has been recently realized in the Nano group [Nano2]. We have also examined a scheme for the calculation of different cumulants of current statistics in multiterminal structures, exploiting the quasiclassical Keldysh counting-field method.
We have studied the measurement of a quantum two-level system through a harmonic oscillator (representing a resonant circuit) coupled to it. We have shown that a fast reflection measurement can be used as a direct probe of the quantum state of the system [s2]. This study is closely related to the experiments done in the Nano group.
[s1] Tero T. Heikkilä and Leif Roschier, Cyclostationary measurement of low-frequency odd moments of current fluctuations, Phys. Rev. B 71, 085316 (2005).
[s2] Teemu Ojanen and Tero T. Heikkilä, State-dependent impedance of a strongly coupled oscillator-qubit system, Phys. Rev. B (submitted) (2004) [cond-mat/0501043].