f(R) Black Holes as Heat Engines

With the cosmological constant considered as a thermodynamic variable in the extended phase space, it is natural to study the thermodynamic cycles of the black hole, which is conjectured to be performed using renormalization group flow. We first investigate the thermodynamic cycles of a 4-dimensional asymptotically AdS f(R) black hole. Then we study the thermodynamic cycles of higher dimensional asymptotically AdS f(R) black holes. It is found that when ΔV ? ΔP, the efficiency of isobar-isochore cycles running between high temperature T_H and low temperature T_C will increase to its maximum value, which is exactly the Carnot cycles’ efficiency both in 4-dimensional and in higher dimensional cases. We speculate that this property is universal for AdS black holes, if there is no phase transition in the thermodynamic cycle. This result may deepen our understanding of the thermodynamics of the AdS black holes.     

Thermal source of stimulated radiation

The action of a source of stimulated radiation is investigated under conditions when the energy is supplied from a thermal reservoir. For the three-level system a calculation based on thermodynamic considerations and kinetic equations is carried out. Relations expressing the dependence of the minimum temperature of the hot reservoir, which is necessary for inversion, on the parameters of the system and on the maximum intensity of exciting radiation are found.The expression for the efficiency of conversion of thermal energy into stimulated radiation is _max<(1–T ₀/T)(A ₃₂–A ₂₁)/(A ₃₂+A ₃₁).This efficiency is always lower than the Carnot efficiency and depends also on the value of the Einstein coefficients for spontaneous emission between different levels.The author heartily thanks M. Trlifaj, K. Pátek and A. Fousková for stimulating discussions.     

Holographic Entanglement Entropy of the BTZ Black Hole

We investigate quantum entanglement of gravitational configurations in 3D AdS gravity using the AdS/CFT correspondence. We derive explicit formulas for the holographic entanglement entropy (EE) of the BTZ black hole, conical singularities and regularized AdS₃. The leading term in the large temperature expansion of the holographic EE of the BTZ black hole reproduces exactly its Bekenstein-Hawking entropy S _BH , whereas the subleading term behaves as ln S _BH . We also show that the leading term of the holographic EE for the BTZ black hole can be obtained from the large temperature expansion of the partition function of a broad class of 2D CFTs on the torus. This result indicates that black hole EE is not a fundamental feature of the underlying theory of quantum gravity but emerges when the semiclassical notion of spacetime geometry is used to describe the black hole.     

Charged torus-like black holes as heat engines

We investigate the thermodynamical properties of charged torus-like black holes and take it as the working substance to study the heat engines. In the extended phase space, by interpreting the cosmological constant as the thermodynamic pressure, we derive the thermodynamical quantities by the first law of black hole thermodynamics and obtain the equation of state. Then, we calculate the efficiency of the heat engine in the Carnot cycle as well as the rectangular cycle,and investigate how the efficiency changes with respect to volume. In addition, to avoid a negative temperature, we emphasize that the charge of this black hole cannot be arbitrary. Last,we check the calculation accuracy of a benchmark scheme and discuss the upper bound and lower bound for charged torus-like black hole in the scheme.     

Thermodynamic estimation of cooling efficiency using an electrocaloric solid-state line

A thermodynamic cycle in a solid-state cooling line including two ferroelectric capacitors which exhibit the electrocaloric (EC) effect is considered. Expressions are derived for determining the cooling factor and the efficiency of the EC cooling line in terms of the Carnot cycle. Numerical estimates obtained for barium-strontium titanate ferroelectric capacitors make it possible to determine the cooling efficiency upon a change in temperature by ΔT = 2 K. At the initial temperature of 272 K, the efficiency is 0.6 Carnot, which considerably exceeds the efficiency of vapor-compression refrigerators.     

Efficiency of reverse cycles

It is demonstrated that the generally accepted treatment of the second law of thermodynamics is incorrect when the statement of the maximum limiting efficiency of the forward Carnot cycle is applied to the reverse cycles. An analysis of reversible cycles compared with the Carnot cycle shows that the reverse Carnot cycle has the lowest efficiency of all reverse cycles. A new characteristic is proposed — the thermal efficiency of reverse cycles, and a generalized theorem is put forward for the additivity of the thermal efficiencies of the forward and reverse cycles. A formulation of the second law of thermodynamics is suggested from the point of view of the efficiency of reverse cycles. Zh. Tekh. Fiz. 69, 11–14 (June 1999)     

Magnetic properties of Co-impregnated zeolites

The structure and magnetic properties of Co-containing zeolites prepared by wet impregnation were investigated. The samples were calcined and then reduced in flowing H₂. The samples studied have large saturation magnetization due to the presence of cubic Co particles over a wide range of sizes. The zero field cooling-field cooling curves show a sharp magnetization peak with a blocking temperature around 7 K followed by an exponential decay and two other peaks—of much lower amplitude—around 160 and 280 K. The low temperature peak is analyzed considering first, at T_crit, thermal relaxation toward equilibrium over an energy barrier, with increasing viscosity S with T. Above T_crit relaxation does not occur and viscosity abruptly goes to zero. The behavior of the smallest Co particles is unusual above the blocking temperature.     

High-field interlayer tunnelling transport in layered cuprates: Uncovering the pseudogap state

In high temperature (high T _c ) cuprate superconductors the gap in the electronic density of states is not fully filled at T _c ; it evolves into a partial (pseudo)gap that survives way beyond T _c , challenging the conventional views. We have investigated the pseudogap phenomenon in the field-temperature (H-T) diagram of Bi₂Sr₂CaCu₂O_{8 + y} over a wide range of hole doping ( ). Using interlayer tunneling transport in magnetic fields up to 60 T to probe the density-of states (DOS) depletion at low excitation energies we mapped the pseudogap closing field H _pg . We found that H _pg and the pseudogap onset temperature T ^* are related via a Zeeman relation , irrespective of whether the magnetic field is applied along the c-axis or parallel to CuO₂ planes. In contrast to large anisotropy of the superconducting state, the field anisotropy of H _pg is due solely to the g-factor. Our findings indicate that the pseudogap is of singlet-spin origin, consistent with models based on doped Mott insulator.Received: 2 February 2004, Published online: 10 August 2004PACS: 74.25.Dw Superconductivity phase diagrams - 74.25.Fy Transport properties (electric and thermal conductivity, thermoelectric effects, etc.) - 74.72.Hs Bi-based cuprates     

Tunneling Effect of Two Horizons from a Reissner-Nordstrom Black Hole

The understanding of possible role played by the inner horizon of black holes in black hole thermodynamics is still somewhat incomplete. By adopting Damour-Ruffini method and the thin film model which is developed on the base of brick wall model suggested by ’t Hooft, we calculate the temperature and the entropy of the inner horizon of a R-N black hole. We conclude that the temperature of inner horizon is positive and the entropy of the inner horizon is proportional to the area of the inner horizon. In addition, the cut-off factor is 90β, which is same in calculation of the entropy of the outer horizon. So, we prove the existence of thermal characters of the inner horizon. Then, we discuss that if the contribution of the inner horizon is taken into account to the total entropy of the black hole, the Nernst theorem can be satisfied. At last, we study the tunneling effect including the inner horizon of the Reissner-Nordstrom black hole. We calculate the tunneling rate of the outer horizon Γ₊ and the inner horizon Γ₋. The total tunneling rate Γ should be the product of the rates of the outer and inner horizon, Γ=Γ₊⋅Γ₋. We find that the total tunneling rate is in agreement with the Parikh’s standard result, Γ→exp (ΔS _BH ), and there is no information loss.     

Thermodynamics Properties of the Inner Horizon of?a?Kerr-Newman Black Hole

In this paper, we study the thermal properties of the inner horizon of a Kerr-Newman black hole. By adopting Damour-Ruffini method and the thin film model which is developed on the base of brick wall model suggested by ’t Hooft, we calculate the temperature and the entropy of the inner horizon of a Kerr-Newman black hole. We conclude that the temperature of inner horizon is positive and the entropy of the inner horizon is proportional to the area of the inner horizon. The cut-off factor is same as it in calculation of the entropy of the outer horizon, 90β. In addition, we write the integral and differential Bekenstein-Smarr formula as the parameters of the inner horizon. Then, we discuss that if the contribution of the inner horizon is taken into account to the total entropy of the black hole, the Nernst theorem can be satisfied. At last, We calculate the tunneling rate of the outer horizon Γ₊ and the inner horizon Γ₋. The total tunneling rate Γ should be the product of the rates of the outer and inner horizon, Γ=Γ₊⋅Γ₋. We find that the total tunneling rate is in agreement with the Parikh’s standard result, Γ→exp (ΔS _BH ), and there is no information loss.     

Thermodynamics and phase transition of the Reissner–Nordstr?m black hole surrounded by quintessence

We investigate thermodynamics and phase transition of the Reissner–Nordstr?m black hole surrounded by quintessence. Using thermodynamical laws of black holes, we derive the expressions of some thermodynamics quantities for the Reissner–Nordstr?m black hole surrounded by quintessence. The variations of the temperature and heat capacity with the entropy were plotted for different values of the state parameter related to the quintessence, ω _q , and the normalization constant related to the density of quintessence c. We show that when varying the entropy of the black hole a phase transition is observed in the black hole. Moreover, when increasing the density of quintessence, the transition point is shifted to lower entropy and the temperature of the black hole decreases.     

Holographic heat engine efficiency of hyperbolic charged black holes

We consider a four-dimensional charged hyperbolic black hole as working matter to establish a black hole holographic heat engine, and use the rectangular cycle to obtain the heat engine efficiency. We find that when the increasing of entropy is zero, the heat engine efficiency of the hyperbolic black hole becomes the well-known Carnot efficiency. We also find that less charge corresponds to higher efficiency in the case of $\tilde{q}>0$. Furthermore, we study the efficiency of the flat case and spherical case and compare the efficiency with that of the hyperbolic charged black holes. Finally, we use numerical simulation to study the efficiency in benchmark scheme.     

Effect of thermal inhomogeneity on the performance of a Brownian heat engine

We explore the effect of thermal inhomogeneity on the performance of a Brownian heat engine by considering exactly solvable models. We first consider a Brownian heat engine which is modeled as a Brownian particle in a ratchet potential moving through a highly viscous medium driven by the thermal kick it receives from a linearly decreasing background temperature. We show that even though the energy transfer due to kinetic energy is neglected, Carnot efficiency cannot be achieved at quasistatic limit. At quasistatic limit, the efficiency for such a Brownian heat engine approaches the efficiency of endoreversible engine η = 1 ? √T _c /T _h [F.L. Curzon, B. Ahlborn, Am. J. Phys. 43, 22 (1975)]. Moreover, the dependence of the current, the efficiency and the coefficient of performance of the refrigerator on the model parameters is also explored via Brownian dynamic simulations and analytically. We show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature [M. Asfaw, M. Bekele, Eur. Phys. J. B 38, 457 (2004), M. Asfaw, M. Bekele, Physica A 384, 346 (2007)]. Furthermore, for a Brownian heat engine driven by a piecewise constant temperature, we show that systematic removal of the inhomogeneous medium leads to a homogeneous medium with a uniform temperature where the effect of temperature inhomogeneity is replaced by an effective load.     

Magnetic properties of magnetite thin films close to the Verwey transition

Temperature dependence of the magnetic properties of magnetite thin film across the Verwey transition has been investigated. As the temperature is decreased, the magnetization of the film in a fixed field showed a sharp decrease close to the Verwey transition temperature (T_v). The M–H loops of the film have been recorded at various temperatures below and above T_v. It is found that film does not saturate at any temperature and saturation becomes more difficult below T_v. While cooling through T_v, the extrapolated value of magnetization to infinite field (Q), calculated from the numerical fit 4πM=Q [1−(H*/H)^1/2], does not show a drop, but the coefficient indicating difficulty in saturation (H*) shows a sharp rise as does the coercivity.     

Inelastic scattering of phonons by quadrupole defects with internal degrees of freedom

We solve the quantum mechanical problem of the inelastic scattering of phonons by a quadrupole defect in a crystal lattice for the case of solid parahydrogen whose matrix contains pair complexes of H₂ orthomolecules. By employing the pseudospin approximation for the operator of the energy of quadrupole-quadrupole interaction of the molecules in an orthopair we derive an effective Hamiltonian that describes the interaction of phonons with a pair quadrupole orthodefect in the lattice. We set up the scattering matrix and calculate the effective phonon relaxation time τ(ω, T) as a function of the frequency ω and the crystal temperature T. We also find that a pair quadrupole defect, which has a complicated system of levels, can be replaced by an effective two-level system with temperature-dependent parameters. The fact that a pair quadrupole orthocluster has internal degrees of freedom results in a resonant scattering peak near a certain critical temperature T ₀. Our estimates for H₂ yield T ₀≃ 6–7 K. Finally, we discuss the contribution of this mechanism to the low-temperature thermal conductivity of solid hydrogen. Zh. éksp. Teor. Fiz. 114, 555–569 (August 1998)     

A nonfrustrated magnetoelectric with incommensurate magnetic order in magnetic field

We discuss a model nonfrustrated magnetoelectric in which a sufficiently strong magnetoelectric coupling produces an incommensurate magnetic order leading to ferroelectricity. Properties of the magnetoelectric in the magnetic field directed perpendicular to the wave vector describing the spin helix are considered in detail. Analysis of the classical energy shows that in contrast to the naive expectation, the onset of ferroelectricity occurs at a field H _c1 that is lower than the saturation field H _c2. We have H _c1 = H _c2 at large enough magnetoelectric coupling. We show that at H = 0, ferroelectricity occurs at T = T _FE < T _N. A qualitative discussion of the phase diagram in the H-T plane is presented within the mean-field approach. The text was submitted by the author in English.     

Black hole/string transition for the small Schwarzschild black hole of AdS 5 × S5 and critical unitary matrix models

In this paper we discuss the black hole–string transition of the small Schwarzschild black hole of AdS ₅×S⁵ using the AdS/CFT correspondence at finite temperature. The finite temperature gauge theory effective action, at weak and strong coupling, can be expressed entirely in terms of constant Polyakov lines which are SU(N) matrices. In showing this we have taken into account that there are no Nambu–Goldstone modes associated with the fact that the 10-dimensional black hole solution sits at a point in S⁵. We show that the phase of the gauge theory in which the eigenvalue spectrum has a gap corresponds to supergravity saddle points in the bulk theory. We identify the third order N=∞ phase transition with the black hole–string transition. This singularity can be resolved using a double scaling limit in the transition region where the large N expansion is organized in terms of powers of N^-2/3. The N=∞ transition now becomes a smooth crossover in terms of a renormalized string coupling constant, reflecting the physics of large but finite N. Multiply wound Polyakov lines condense in the crossover region. We also discuss the implications of our results for the resolution of the singularity of the lorenztian section of the small Schwarzschild black hole.     

First XANES evidence of a disorder–order transition in a spinel ferrite compound: nanocrystalline ZnFe2O4

In situ Zn K‐edge XANES experiments were performed to investigate the thermal evolution of the non‐equilibrium state in nano‐sized ZnFe₂O₄. The initially disordered ferrite was annealed under oxygen atmosphere and kept at temperatures of 673, 773 and 873 K. Modifications of the XANES features allowed the direct detection of the Zn local surrounding changes from O_h to T_d symmetry. Quantitative analyses of these results were performed by using the principal‐component analysis approach. The ferrite inversion does not change until the activation barrier is overcome at T_a = 585 K. Above T_a, the Zn ions continuously change their environment to their normal equilibrium state. Isothermal treatments confirm that the Zn transference follows a first‐order kinetic process. In addition, the thermal treatment produces a partial recrystallization that increases the average grain size from 13 to 50 nm and reduces the microstrain. The room‐temperature magnetic state changes from ferrimagnetic to paramagnetic, while the blocking temperature increases after the treatment.     

A black hole spectral signature

An accreting black hole is, by definition, characterized by the drain. Namely, the matter falls into a black hole much the same way as water disappears down a drain — matter goes in and nothing comes out. As this can only happen in a black hole, it provides a way to see “a black hole”, an unique observational signature. The accretion proceeds almost in a free-fall manner close to the black hole horizon, where the strong gravitational field dominates the pressure forces. In this paper we present analytical calculations and Monte-Carlo simulations of the specific features of X-ray spectra formed as a result of upscattering of the soft (disk) photons in the converging inflow (CI) into the black hole. The full relativistic treatment has been implemented to reproduce these spectra. We show that spectra in the soft state of black hole systems (BHS) can be described as the sum of a thermal (disk) component and the convolution of some fraction of this component with the CI upscattering spread (Greens) function. The latter boosted photon component is seen as an extended power-law at energies much higher than the characteristic energy of the soft photons. We demonstrate the stability of the power spectral index over a wide range of the plasma temperature 0 – 10 keV and mass accretion rates (higher than 2 in Eddington units). We also demonstrate that the sharp high energy cutoff occurs at energies of 200–400 keV which are related to the average energy of electrons m_ec² impinging upon the event horizon. The spectrum is practically identical to the standard thermal Comptonization spectrum when the CI plasma temperature is getting of order of 50 keV (the typical ones for the hard state of BHS). In this case one can see the effect of the bulk motion only at high energies where there is an excess in the CI spectrum with respect to the pure thermal one. Furthermore we demonstrate that the change of spectral shapes from the soft X-ray state to the hard X-ray state is clearly to be related with the temperature of the bulk flow. In other words the effect of the bulk Comptonization compared to the thermal one is getting stronger when the plasma temperature drops below 10 keV. We clearly demonstrate that these spectra emerging from the converging inflow are a inevitable stamp of the BHS where the strong gravitational field dominates the pressure forces.     

Field and temperature dependence of intergranular hysteresis in YBa2Cu3O7

We have studied the variation of low field magnetization hysteresis in YBa₂Cu₃O₇ as a function of the maximum magnetic field applied during a hysteresis cycle (1 G<H _max<7.3 G) and also as a function of temperature (77 K<T<95 K). The remnant magnetization is studied as a function ofH _max andT and the measured dependences are explained using the extended critical state model. The potential of this technique as a contactless method of probing the temperature dependence ofJ _c is discussed.