Ettore majorana foundation and centre for scientific culture

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НазваниеEttore majorana foundation and centre for scientific culture
Дата конвертации16.02.2013
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Heat conduction in disordered harmonic lattices with energy conserving noise

We study the nonequilibrium steady state of disordered harmonic lattices whose Hamiltonian dynamics is supplemented by a stochastic flipping of the momentum of every particle. This dynamics conserves energy but not momentum. The one-body and pair correlations in this system are shown to be the same as those obtained for a model with self-consistent reservoirs, after an appropriate mapping of parameters. Results are presented, from numerics and simulations of a 1D system, on the dependence of the heat flux on the system size and on the flipping rate. The form of kappa at small flipping rates will be discussed.


Finite-time efficiency of small devices

Due to environment fluctuations, it is often natural to describe small systems by stochastic dynamics. With very few physical assumptions and the correct identification of entropy production, the stochastic dynamics provides a consistent nonequilibrium thermodynamics description of small systems. I will show that such description enables the study of thermodynamic efficiencies of small devices in finite time. Applications to simple models such as thermoelectric quantum dots and photoelectric cells will be presented.


Zeropower: a Europe-wide initiative for nanoscale energy management

Nanoscale energy management is a new, exciting field that is gaining increasing importance with the realization that a new generation of micro-to-nanoscale devices aimed at sensing, processing, actuating and communication will not be possible without solving the powering issue. European Commission has founded initiatives aimed at coordinating research efforts around this topic. The scientific objective is to study energy efficiency with the specific aim of identifying new directions for energy-harvesting technologies at the nanometer and molecular scale. For this objective the study of heat control and thermoelectric efficiency is of paramount importance.


From ballistic to hopping transport in topologically disordered quantum systems

We consider tight-binding quantum single-particle models on topologically completely disordered "lattices". Our goal is to find transport parameters such as diffusion coefficients, mean free paths, etc. Although there is no true momentum space, the question may be addressed on the basis of projection operator techniques and/or Boltzmann equations, linear response, etc. We find that for some models diffusion coefficients are in accord with classical random-walk scenarions, furthermore mean free paths may vary from about one to very many mean site distances.


Heat transport in superconducting nanostructures and two-dimensional electron gas systems

In recent times, the interest in thermoelectric phenomena in mesoscopic systems has become more and more apparent [1]. In this context, solid-state refrigeration is particularly under the spotlight. Promising solid-state refrigeration schemes operating at sub-Kelvin temperatures rely on superconducting nanostructures [1-3], and have shown to yield remarkable electron and phonon temperature reduction. In these systems, a normal metal region is coupled to a superconductor through an insulating tunnel barrier. Quasiparticle cooling occurs thanks to the existence of the superconducting gap, which allows only the more “hotter” electrons to escape from the normal metal region. In the first part of this presentation we will show the implementation of all-superconducting electron nanorefrigerators based on the V/AlOx/Al materials combination. The structure were realized with standard electron-beam lithography and shadow-mask evaporation of metals. Notably, electron temperature reduction down to around 400 mK starting from a bath temperature of 1 K were routinely achieved in such devices. This makes V-based superconducting refrigerators promising for the implementation of the high-temperature stage in cascade solid-state cooling.

In the second part of this presentation we shall show that a lateral quantum dot (QD) defined in a GaAs/AlGaAs heterostructure can be used for the detection of local temperature within a two-dimensional electron gas (2DEG) microdomain. Our method relies on the observation that a temperature bias across the QD changes the functional form of the Coulomb blockade resonant peaks. In our experimental system, the QD is coupled to a micrometer-sized electron domain which can be heated by DC current injection through two quantum point contacts coupled to the reservoir. This structure is an ideal platform for the investigation of the energy relaxation mechanisms in 2DEGs, for instance, the electron-phonon interaction. To this end, we will show that the power transferred from the electrons to the phonon bath is proportional to the fifth power of the temperature, as expected for the screened piezoelectric interaction, and we provide a measure of the relative coupling constant.

[1] F. Giazotto, T. T. Heikkila, A. Luukanen, A. M. Savin, and J. P. Pekola, Rev. Mod. Phys. 78, 217 (2006).

[2] M. Nahum, T. M. Eiles, and J. M. Martinis, Appl. Phys. Lett. 65, 3123 (1994).

[3] M. M. Leivo, J. P. Pekola, and D. V. Averin, Appl. Phys. Lett. 68, 1996 (1996).


Hot quantum system interacting with cold one: The chronicle of mutual equilibration

If we bring two systems, hot and  cold, into contact, heat starts to flow from the hot system to the cold one, and after a long enough time, we find them both at the same temperature. While the first part of the statement constitutes one of the most fundamental laws of nature, the Second Law of Thermodynamics, the second part is a common belief, i.e. it sounds reasonable to the most of scientists. Any attempt to prove the last part of the statement by using laws of dynamics, classical or quantum, unavoidably leads to the following challenge: How does the irreversible equilibration occur when the evolution is governed by time-reversible equations? This question has sparked recently a new wave of activity in the quantum domain, where the thermalization conundrum has been studied either at the micro-level of a single isolated system, or at the macro-level, with the system of interest coupled to a giant quantum bath, -- e.g. in the extreme to the rest of the Universe.

Here we show that two identical but  finite quantum systems, prepared initially at different temperatures, isolated from the environment and then brought into contact, relax to equilibrium states characterized by the same temperature, passing through a chain of intermediate thermal states. The quantum equilibration process reveals the property of typicality, so that almost every pair of pure initial states, randomly sampled from a set of typical states, replicates a relaxation pathway with high accuracy. By this we demonstrate that the archetypical thermodynamic process such as a its temperature equilibration can be reproduced within an  isolated quantum system in a pure state [1].

[1]   A. V. Ponomarev, S. Denisov and P. Hänggi, Thermal equilibration between two quantum systems [arXiv:1004.2232]; v3 -- includes the supplementary material.


Thermal transport and thermoelectric coefficients near the Anderson transition and in molecular junctions

We start by reviewing thermal and thermoelectric linear transport, including the various coefficients the symmetry relations among them (Onsager) and what determines their magnitudes. Applications will be briefly mentioned along with the requirements on the above coefficients

Next, the Anderson localization transition will be considered at finite temperatures. This includes the electrical conductivity as well as the electronic thermal conductivity and the thermoelectric coefficients 1-3. The latter becomes relatively large at low temperatures near the transition, its interesting critical behavior is found. A method for characterizing the conductivity critical exponent, an important signature of the transition, using both the conductivity and thermopower measurements, is outlined.

Finally, the thermoelectric transport through a molecular bridge 4 –a model nanosystem-- will be discussed, with an emphasis on the effects of inelastic processes of the transport electrons caused by the coupling to the vibrational modes of the molecule. In particular it is found that when the molecule is coupled to a thermal bath of its own, which may be at a temperature different from those of the electronic reservoirs, a heat current between the molecule and the reservoir can be generated by the usual electric current. Expressions for the transport coefficients governing this conversion and similar ones are derived, and a possible scenario for increasing their magnitudes is outlined. This interesting case of three terminals with two types of carriers presents novel possibilities.

[1] M. Cutler and N. F. Mott, Phys Rev. 181, 1336 (1969).

[2] U. Sivan and Y. Imry, Phys Rev B33, 551 (1986).

[3] Y. Imry and A. Amir, The localization transition at finite temperatures: electric and thermal transport, in 50 years of Anderson Localization, edited by E. Abrahams (World Scientific, Singapore, 2010) in press, arXiv:1004.09666.

[4] O. Entin-Wohlman, Y. Imry and A. Aharony, Three-terminal thermoelectric transport through a molecular junction, arXiv:1005.39400.


Nonreciprocal wave propagation in a nonlinear system

A mechanism for asymmetric (nonreciprocal) wave transmission in layered nonlinear, non mirror-symmetric systems is presented. As a reference model, we consider wave solutions of the one-dimensional Discrete Nonlinear Schr\"odinger equation with spatially varying coefficients embedded in an otherwise linear lattice. We construct class of exact extended solutions such that waves with the same frequency and incident amplitude impinging from left and right directions have very different transmission coefficients. The effect arises already for the simplest case of two nonlinear layers and is associated with the shift of nonlinear resonances. Increasing the number of layers considerably increases the complexity of the family of solutions. Numerical simulations of asymmetric wavepacket transmission are also presented.


Nonlinear thermoelectric effects in semiconductors nanostructures

Low-dimensional semiconductor systems, such as quantum dots (0D), ideal nanowires (1D), or 2D energy barriers can be used to select the energy of electrons that can traverse these structures. Such an effect is required for any thermoelectric (TE) effect, but the additional tunability afforded by artificial low-D systems offers the opportunity to optimize the electronic conversion efficiency.

The key property of low-D systems that allows energy filtering – namely a strongly energy dependent transmission function for electrons – as well as the small overall size of such systems, also implies that they are very easily driven into nonlinear response. Specifically, their thermovoltage and thermocurrent can be strongly nonlinear in the temperature differential. This is important, first, because such behavior msut be understood to be able optimize the performance of low-D TE systems. Secondly, nonlinear behavior can in principle be exploited, for example, for rectification of heat flow.

We will present experimental data and theoretical modeling of nonlinear thermoelectric behavior in quantum dots embedded into semiconductor nanowires.


Heat flow in nanostructures

Nanostructure tends to reduce the thermal conductivity, due to the thermal boundary resistance at interfaces. Our recent work on thermal boundary resistance will be reviewed, and compared to experiment. We were the first to predict reduced thermal conductivity in the cross-plane direction, and the first to predict that the cross-plane thermal conductivity had a minimum when graphed vs. layer thickness. We also show that electron and phonon temperatures were unequal during heat flow due to Kapitza resistance. We have a new theory of thermal resistance at the interface between a metal and an insulator, based on the image potential.


Thermodynamics of small systems: Emergence of irreversibility

We investigate irreversibility from an operational point of view. For this purpose we study a bi-partite quantum system under unitary dynamics but seen from the perspective of one subsystem of varying size only and subject to perturbations of the respective Hamiltonian. We use the quantum fidelity as a distance measure of two states. For the whole system a perturbation induces instability, but no preferred direction of time yet. We show that an arrow of time shows up only when focusing on a small enough subsystem and long enough evolution times. This approach is exemplified by a numerical simulation of a finite spin network, for which we see how irreversibility emerges locally as we change the partitioning.

[1] G. Waldherr and G. Mahler, EPL 89, 40012 (2010)


Heat transport and cooling in superconducting and metallic nanostructures

We discuss recent experiments investigating heat transport in superconducting electronic circuits and metallic nanostructures. Heat transported by electromagnetic radiation governs the energy exchange of an electronic system with the environment [1,2]. This effect is deployed in our recent work to remotely cool a metallic island. In these experiments, heat conduction is independent of material parameters and the maximum value of heat transport is set by the fundamental quantum of thermal conductance.Heat pumped in a cyclic RF-cooler [3] with a hybrid superconducting-isolator-normal-metal device combines the ideas of a classical solid state coolers with the Coulomb blockade effect.Recent experiments show that heat causes the hysteresis in the transport properties of superconductor-normal-metal-superconductor (S-N-S) junctions at low temperatures. Here, the electron temperature increase is governed by the thermal resistance of the superconducting electrodes of the junction [4]. We find that the thermal conductance of a short superconducting wire is strongly enhanced beyond the BCS value due to the inverse proximity effect [5].Finally we highlight the impact of the findings on practical devices.

[1] M. Meschke, W. Guichard, and J. P. Pekola, Nature 444, 187 (2006).
[2] A. V. Timofeev, M. Helle, M. Meschke, M. Möttönen, and J. P. Pekola, Phys. Rev. Lett. 102, 200801 (2009).

[3] S. Kafanov, A. Kemppinen, Yu. A. Pashkin, M. Meschke, J. S. Tsai, and J. P. Pekola, Phys. Rev. Lett. 103, 120801 (2009).

[4] H. Courtois, M. Meschke,J. T. Peltonen, and J. P.  Pekola, Phys. Rev. Lett. 101, 67002 (2008).

[5] J .T. Peltonen, P. Virtanen, M. Meschke, J.V. Koski, T.T. Heikkilä, and J.P. Pekola, Phys. Rev. Lett. 105, 097004 (2010).


Heating, heat conduction and cooling in molecular junctions

Heating in molecular conduction junction depends on the balance between the rate of heat deposit by the electronic current and the efficiency of heat conduction away from the junction. I will review our recent work on such processes, then focus on models for current induced cooling in such systems.

[1] D. Segal, A. Nitzan, and P. Hanggi, J. Chem. Phys. 119, 6840 (2003).

[2] D. Segal and A. Nitzan, Phys. Rev. E 73, 026109 (2006).

[3] M. Galperin, M. Ratner, and A. Nitzan, Phys. Rev. B 75, 155312 (2007).

[4] M. Galperin, K. Saito, A. V. Balatsky, et al., Phys. Rev. B 80, 115427 (2009).

[5] P. R. Schiff and A. Nitzan, Chemical Physics, in press (2010).


Thermal enhancement of interference effects in quantum point contacts

The images obtained by measuring the conductance of a quantum point contact when the charged tip of an AFM microscope is scanned in its vicinity exhibit fringes spaced by half the Fermi wavelength. Inceasing the temperature, the visibility of these fringes can be strongly enhanced in the vicinity of a point contact opened near the edges of a quantized conductance plateau. The origin of this unusual thermal enhancement of interference effects is explained assuming a simplified model


On some exactly solvable cases of far from equilibrium transport in many-body quantum chains

An approach towards exact solution of many-body open quantum systems based on Fock spaces of density operators shall be discussed. Such treatment is particularly well suited for studying Lindblad or Redfield master equations of quadratic fermionic or bosonic chains where certain explicit reasults on heat transport and non-equilibrium phase transitions can be obtained. As an example we outline XY spin 1/2 chain. Furthermore, one is able to write down explicit non-equilibrium steady states for some interacting quantum spin chains, such as XX chain with dephasing noise, fermionic Hubbard chain, or Heisenberg XXZ spin 1/2 chain for which we analytically reproduce recently numerically observed negative-differential-conductance.


Thermalization and ergodicity in many-body open quantum systems

Recent experiments with ultracold atomic gases raised an intense theoretical activity focused on some fundamental aspects of nonequilibrium physics in strongly correlated quantum systems. In particular, the observation of absence of thermalization in closed integrable systems put forward some questions related to the integrability issue in such systems. As a matter of fact, the nonequilibrium dynamics of a closed chaotic system is expected to thermalize at the level of individual eigenstates; by contrast, for systems with non trivial integrals of motion, steady states usually carry memory of the initial conditions and are not canonical.

Much less is known about the relaxation to the steady state for open quantum systems. We have performed extensive numerical investigations in many-body quantum systems locally coupled via Lindblad equation to an external bath. We provide evidence of the fact that quantum chaotic systems do thermalize, that is, after long time they reach an invariant ergodic state which is in the bulk well approximated by the grandcanonical state. Moreover, the resulting ergodic state does not depend on the details of the baths. On the other hand, for integrable systems the invariant ergodic state does depend on the bath and is in general different from the grandcanonical state.

Our method is applicable also to non-equilibrium situations, by locally coupling a system to two or several baths at different temperatures and chemical potentials. This may open significant new perspectives in the simulation of quantum transport in many-body quantum systems in contact with thermochemical baths.


Dimensionality dependence of phononic transport  

We perform nonequilibrium simulations of heat conduction in a three dimensional anharmonic lattice. By studying slabs of length N and width W, we examine the cross-over from one-dimensional to three dimensional behavior of the thermal conductivity. We find that for large N, the cross-over takes place at a small value of the aspect ratio W/N. From our numerical data we conclude that the three dimensional system has a finite non-diverging thermal conductivity and thus provide the verification of Fourier's law in a system without pinning. We compare it with recent dimensional crossover experiments in graphene flakes.


Heat engines and thermal conduction: An information theory model

We construct a minimal model of a heat engine (or a Maxwell's demon) using information theory concepts, and employ it for analyzing the operation principles of finite-time thermodynamic machines. In our model irreversible energy dissipation is attributed to information transfer within the engine's communication channels, compensating entropy decrease in the system. The model serves as a testbed for studying fundamental topics in thermodynamics. In particular, we examine the universality of the maximum power efficiency and its relationship to the Carnot efficiency. The model can be extended, serving as an abstract setting for exploring basic topics in nonlinear heat conduction. We demonstrate that due to the irreversible loss of energy at the contacts, a junction conduction becomes nonlinear.


Transient charge and energy transport in thermoelectric devices

Thermoelectric devices can have enhanced cooling under pulsed operation since the time response of Peltier effect at the contact is faster than Joule heating in the volume of the thermoelectric element. We present experimental transient cooling of 3 microns thick Si/SiGe superlattice refrigerators using thermoreflectance technique [1,2]. Thermal images are obtained with submicron spatial, 0.1C temperature and nanosecond time resolution. We will then describe the impulse electro-thermal response of thermoelectric materials from a fundamental point-of-view. It has been shown that materials with high thermoelectric figure-of-merit should have a strong coupling between charge and energy transport at the microscale [4,5]. In ballistic heat conduction regime, one can also observe oscillation in energy transport at very short time scales due to the Bragg reflections from Brillouin zone boundaries.

[1] A. Shakouri and M. Zeberjadi, "Chapter 9: Nanoengineered Materials for Thermoelectric Energy Conversion," in: Thermal Nanosystems and Nanomaterials, ed. by Volz, S., Springer, pp. 225-299 (2009).

[2] Y. Ezzahri, J. Christofferson, G. Zeng and A. Shakouri, "Short time transient thermal behavior of solid-state microrefrigerators," J. Appl. Phys. 106, 114503 (2009).

[3] B. S. Shastry, “Electrothermal transport coefficients at finite frequencies,'' Rep. Prog. Phys. 72, 016501 (2009).

[4] Y. Ezzahri and A. Shakouri, "Ballistic and Diffusive Transport of Energy and Heat in Metals," Physical Review B79, 184303 (2009).


Thermal transport and thermoelectric energy conversion in nanostructured and complex materials

High and low thermal conductivities, respectively, are desirable for increasing the energy efficiency of electronic and thermoelectric devices. Recently, ultrahigh thermal conductivity has been reported in mechanically exfoliated monolayer graphene. Our recent measurements show that even large-area graphene grown by chemical vapor deposition possesses higher thermal conductivity than graphite, but contact with a dielectric support suppresses the thermal conductivity of graphene because of phonon leakage across the interface. Despite the still high thermal conductivity of supported graphene, spatial mapping of the low-frequency phonon temperature distribution in graphene electronic devices reveals that the major heat dissipation path is across the dielectric support instead of lateral heat spreading along the graphene to the metal electrodes. In the other end of the thermal conductivity spectrum, our measurements reveal highly anisotropic thermal transport in disordered-layered thin films that were found to possess ultralow cross-plane thermal conductivity. We have also found that the lattice thermal conductivity of nanowire structures is suppressed considerably for III-V semiconductors, but only slightly for bismuth telluride with already useful thermoelectric figure of merit (ZT). In contrast, the thermal conductivity of higher manganese silicide (HMS) nanowires can be suppressed from the already low bulk values to the amorphous limit. This finding of a glassy thermal conductivity in a crystal is attributed to the combined effect of a complex crystal structure and phonon-interface scattering in the HMS nanowires, and points to a potential approach to enhancing the ZT.


Disorder driven thermal transport in hard and soft matter

We discuss two aspects of disorder in hard and soft matter. In the first case, engineered roughness on silicon nanowires leads to a dramatic reduction in thermal conductivity. We show how values between 1 and 10 W/mK at room temperature may be explained using a theory of multiple scattering of phonons at the boundaries. We discuss our recent efforts at understanding and exploiting thisphenomena in thermoelectric applications. In the second materials system, we investigate the conduction of heat in ultrathin (<10 nm) films of amorphous fluorocarbons to experimentally show that thermal conductivity obeys a percolation law consistent with an existing theory on rigidity percolation. This percolation is atomic scale and is distinct from the typical percolation of thermal resistance in composite materials.


Cooling an electron gas below the lattice temperature using quantum dot energy levels

When measuring low dimensional electron systems at cryogenic temperatures it is often difficult to cool the electrons down to the lattice temperature, because the electric fields used to make the measurements cause electron heating. Unwanted electric fields from environmental noise also can heat the electron bath above that of the lattice. Usually the electrons are cooled to the lattice temperature via emission of phonons, but this process drops off quickly at low temperatures. In this talk I will show how we can make measurements on a two dimensional electron gas in a semiconductor heterostructure, while simultaneously cooling the electrons in that area. This is achieved by using quantum dots at the entrance and exit of the device. By tuning the properties of the dots and the energy levels relative to the Fermi energy in the device, it is possible to inject cold electrons and pull out hot electrons to reduce the spread in the Fermi distribution and cool the electrons below the lattice temperature. This process can also give us important information about the electron-electron scattering rate.


Oxide thermal rectifier and oxide thermoelectric device

A thermal rectifier is a device which conducts heat along one direction more than along the opposite direction, being an equivalent of a diode for electrical current. This sounds like Maxwell's daemon, but various theoretical models have been proposed without violation of the second law of the thermodynamics. In particular, Peyrard has proposed a simple design of this device by making a junction of two materials whose thermal conductivities show different temperature dependence. We succeeded in making a prototype thermal rectifier using perovskite-type cobalt oxides, and obtained a rectifying coefficient of 1.4 [1]. In the former part of this talk, I will briefly review the current status and future prospects of the thermal rectifier.

Aside from the thermal rectifier, cobalt oxides often show large thermopower, which can be used for thermoelectric materials. The thermoelectric material is a material that converts heat into electric power and vice versa through the thermoelectric phenomena in solids. The origin of the large thermopower is believed to come from the large entropy stored on the d electrons in the cobalt ion, which cannot be realized in conventional semiconductors. In the latter part, I will address a possibility of thermoelectric applications using oxide materials [2, 3].

This work was done through full collaboration with Wataru Kobayashi (Waseda University).

[1] W. Kobayashi et al., Appl. Phys. Lett. 95 (2009) 171905

[2] I. Terasaki et al., Dalton Trans. 39 (2010) 1005

[3] I. Terasaki et al., Materials 3 (2010) 786


Controlling heat conduction in nanostructured materials to enhance the thermoelectric figure of merit

Recent improvements of the thermoelectric figure of merit tend to prove that the most significant progresses are obtained by decreasing thermal conductivity while maintaining electrical properties. We will propose several physical models that use nanostructuration to decrease thermal conductivity most efficiently.

The first concept is based on the attenuation of high frequency phonons in alloys. Porous alloys for instance exhibit drastic heat flux reductions compared to the ones obtained in porous and pure materials at same and rather large (100nm-1micron) pore radii (Phys. Rev. Lett. 104, 115502, 2010). It will also be shown that alloys with scattering grain boundaries can be optimized in terms of thermoelectric properties (J.App.Phys. sub. and in press).

The second concept addresses nanowires manifesting strong phonon surface scattering and therefore notable thermal conductivity decrease (J. of App. Phys., 107, 83503, 2010). Explanations to the abnormal ballistic behaviours at ambient temperature are provided. The low temperature nanowire conductance is also revisited when taking into account the connection to realistic heat baths.

[1] Phys. Rev. B, 77, 233309, 2008 and Phys. Rev. B in press).


Open issues on the transport phenomena of 1D quantum magnets

I will discuss recent theoretical developments on the dynamics of one dimensional quantum magnets [1]. In particular, I will focus on open issues and controversial results related to the finite temperature transport of integrable models [2]. These singular systems are commonly used in the description of quasi-one dimensional materials. They are recently attracting interest in connection to experiments, following the discovery of unusual thermal conductivity in quasi-1D magnetic materials [3].

[1] X. Zotos, J. Phys. Soc. Jpn. v.74, 173 (2005).

[2] X. Zotos, F. Naef and P. Prelovsek, Phys. Rev. B55, 11029 (1997).

[3] C. Hess, Eur. Phys. J. Special Topics, v.151, 73 (2007).



       G. Akguc Thermo-electric efficiency of rough silicon wires

       P. Borys  An idea of nano-thermal oxygen controller (NATOC)

       S. Buller tba

       M. Feuchter Numeric simulation of the 3-ω-method for measuring thermal

conductivities in thermoelectric materials at the nanoscale

       Z. J. Grzywna and A. Wawrzkiewicz Neodymium channel's structure of NATOC

       O. Karlström Conductance suppression in a spinless 2-level quantum dot

       T. Ojanen Selection-rule blockade and rectification in quantum heat transport

       K. Pawelek On the nano-thickness oxygen supplier (NATOC)

       T. Ruokola Thermal cotunneling in a spin-boson model

       R. Sánchez Transport via correlated fluctuations

       G. Schaller Charge transport through interacting junctions 

       E. Selezneva Enhancement of thermoelectric power in heavily doped

polysilicon thin films upon isochronal annealing

       A. Vezzani Levy-type diffusion on one-dimensional quenched disordered media

       H. Vocca tba  

       M. Vogl From super-radiance to super-transmittance: FCS incoherent transport

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Ettore majorana foundation and centre for scientific culture iconIcsc international centre for scientific culture

Ettore majorana foundation and centre for scientific culture iconОвощи и некоторые съедобные корнеплоды и клубнеплоды Примечания
Рimenta, фенхелю, петрушке, купырю, эстрагону, кресс-салату и майорану садовому (Majorana hortensis или Origanum majorana)

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Ettore majorana foundation and centre for scientific culture iconInternational islamic university malaysia centre for foundation studies

Ettore majorana foundation and centre for scientific culture iconEncyclopaedic visions : scientific dictionaries and enlightenment culture

Ettore majorana foundation and centre for scientific culture iconThis publication is the result of a project jointly funded by the International Development Research Centre and the Rockefeller Foundation

Ettore majorana foundation and centre for scientific culture iconA culture is a massive edifice, large enough to house millions of long lifetimes of artistic endeavor. The question is, how could I engage in a culture

Ettore majorana foundation and centre for scientific culture iconIn this study, I investigated how participating in a scientific research project changed science teachers’ views of scientific inquiry and the nature of

Ettore majorana foundation and centre for scientific culture iconДоклады на зарубежных научных конференциях (тезисы)
Публикаций в журналах вак (publications in scientific journals approved by Russian scientific authorities)

Ettore majorana foundation and centre for scientific culture icon© А. К. Рой, 1985. © The History of Jains, Gitanjali Publishing House, New Delhi, 1985
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