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can be described by a relatively minor extension of the low-energy (infrared) effective theory. The introduction of an infrared thermodynamic variable, describing certain properties of the deep vacuum can be considered as the first step in a bottom-up approach (trying to go from the effective low-energy theory to the fundamental microscopic theory at Planck scale). This simple approach already allowed us to introduce the thermodynamic notion of the vacuum compressibility, which is a new fundamental constant, and to estimate the thermodynamic back reaction on the vacuum by low-energy phenomena. This also allows us to discuss the spectral function of vacuum energy, i.e. the contribution to the vacuum energy from different energy scales.

### Simulation of rotating black hole

G. Volovik

Collaborator: Makoto Tsubota (Osaka City University, Osaka, Japan),

There are many challenges to simulate the phenomena on black holes by using condensed matter systems. One of them is to study an analogy between gravity and superfluidity, in which a superfluid ground state (superfluid vacuum) serves as the analog of the vacuum of relativistic quantum fields, while the flow of the superfluid liquid imitates the metric field acting on ‘relativistic’ quasiparticles (phonons, ripplons, fermionic excitations, etc.). The Hawking radiation from the black holes can be tested in this analogy. In collaboration with the group of professor Tsubota (Osaka, Japan) we suggested to exploit an atomic Bose-Einstein condensate (BEC) to simulate the similar effect – radiation by a rotating black hole, which is known as Zel’dovich - Starobinskii effect. We considered circular motion of a heavy object in a BEC at T = 0 K, and found that even if the linear velocity of the object is smaller than the Landau critical velocity, the object may radiate quasiparticles and thus experience the quantum friction. The radiation process is exactly similar to the radiation by a rotating black hole. This analogy emerges when one introduces the effective acoustic metric for quasiparticles. In the rotating frame this metric has an ergosurface, which is similar to the ergosurface in the metric of a rotating black hole. The calculated dependence of the radiation rate on the position of the ergosurface is in agreement with the Zel’dovich- Starobinskii scenario.

#### THERMAL AND NONEQUILIBRIUM EFFECTS IN NORMAL-SUPERCONDUCTING HETEROSTRUCTURES

Tero Heikkilä, Matti Laakso, Teemu Ojanen, Pauli Virtanen, and Juha Voutilainen

Collaborators: PICO group, M.S. Crosser, J. Huang, F. Pierre, N. O. Birge (Michigan State University), J.C. Cuevas (Autonomous University of Madrid), F. Giazotto (Scuola Normale Superiore, Pisa, Italy), P. Helistö and A. Luukanen (VTT), A.-P. Jauho (Laboratory of Physics, TKK), G. P. Pepe (University of Naples “Federico II”), I. Sosnin, J. Zou and V. Petrashov (Royal Holloway University of London, the UK), and F. K. Wilhelm (University of Waterloo, Canada)

Major part of our work on thermal and nonequilibrium effects is related to the study of these effects in superconducting proximity structures where the superconducting correlations leak into a normal metal, affecting its properties. For example, the whole thermoelectric response of these systems is modified due to this proximity effect. During 2007, we published our studies of the Peltier effect resulting essentially from

Annual Report 2007