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The recent experimental verification of the charge-transfer superexchange mechanism as the microscopic pairing mechanism of high-$T_c$ cuprate superconductivity by Seamus Davis and collaborators\cite{sea} is a tour de force! The correct model for cuprates is the three band Emery model in which oxygen p-orbitals are explicitly taken into account. The doped holes go into these oxygen p-orbitals where they undergo charge-transfer superexchange with unpaired electrons in copper d orbitals. This charge transfer superexchange is the key which leads to bound pairs and superconductivity. In the experimental verification\cite{sea}, the system chosen is $Bi_2Sr_2CaCu_2O_{8+x}$. What is achieved is the direct functional dependence of the local electron pair density ($n_P(r)$) on local charge transfer energy ($\ep_{pd}(r)$) using state of the art single-electron and electron-pair (Josephson) scanning tunneling microscopy. The quantitative functional dependence of $n_P(r)$ on $\ep_{pd}(r)$ matches with that indicated and deduced by theory\cite{t1,t2,t3,t4,t5,t6,t7,t8,t9,t10}. The verdict of the experiment settles the debates on the microscopic mechanisms of the cuprate superconductivity in the clear favor of charge-transfer superexchange mechanism. We discuss this development in brief, and present a simple minded approach to the essence of cuprate superconductivity. We discuss what is settled now, and what is not settled yet. A "theoretical minimum" of the high-$T_c$ problem is also discussed., 7 pages, 3 figures, minor typos corrected

The way the topic of black-body radiation is presented in standard textbooks (i.e. from Rayleigh-Jeans to Max Planck) does not follow the actual historical timeline of the understanding of the black-body radiation problem. Authors believe that a presentation which follows an actual timeline of the ideas (although not a logical presentation of the field) would be of interest not only from the history of science perspective but also from a pedagogical perspective. Therefore, we attempt a concise history of this very interesting field of science., 27 pages, 10 figures

We answer in affirmative the absence of superconductivity in bulk prepared samples of doped infinite-layer Nickelates through a simple magnetostatic model. In an independent approach we also employ Density Functional Theory (DFT) calculations for the same investigation. Our investigations reveal that it is the formation of Nickel clusters and Nickel deficient regions in bulk prepared samples (as opposed to thin films) that leads to the absence of superconductivity in bulk prepared samples.

Recent research\cite{fort} has shown that in the 20th century there is an exponential growth of the number of published scientific papers, but new ideas has only a linear growth with time. The 19th and the first half of the 20th century saw major scientific discoveries. But from the second half of the 20th century, the number of publications far exceeds the number of impactful discoveries. Does an exponentially growing number of publications indicate an element of pathological research? Pressure to publish a large number of papers has led to the phenomena of overproduction, unnecessary fragmentations, overselling, predatory journals (pay and publish), clever plagiarism, and deliberate obfuscation of scientific results so as to sell and oversell. This is harming the healthy scientific culture of passion driven research. It is an urgent problem which needs attention of the whole of the scientific community. Some ways to mitigate these grave problems are discussed., 9 pages; 5 figures; comments are welcomed

A colossal insulator-to-metal transition in high-spin pyrite phase of $MnS_{2}$ has been experimentally observed \cite{colomns2}. There are two possibilities behind this colossal insulator-to-metal transition: (1) migration of $Mn$ electrons to unoccupied $S^{2-}_{2}$ antibonding states under pressure which leads to conducting ligand states and hence metallic transition, and (2) possibility of band crossing transition. We have analyzed this experimental obervation theoretically using a toy statistical model and found that the transition is due to the migration of electrons from the transition metal ions to the ligand sites (i.e. the possibility (1)). The calculated resistivity compares well with the experimental data within the fitting parameters of the model., 5

A toy statistical model which mimics localized-to-itinerant electron transitions is introduced. We consider a system of two types of charge carriers: (1) localized ones, and (2) itinerant ones. There is chemical equilibrium between these two. The solution of the model shows that there is a crossover, at a specific value of a local interaction energy parameter $J$, at which carriers transfer from being itinerant to a localized/mixed valence state. The model has a very crude analogy to the observed $\gamma\rta\alpha$ transition in metal cerium., Comment: 6 pages, 8 figures

A detailed review is given on the evolution of the theory of itinerant magnetism. The self-consistent renormalization (SCR) theory is quite successful in addressing the phenomenon of itinerant magnetism in weakly and nearly ferromagnetic and anti-ferromagnetic materials. It goes beyond the Stoner and random phase approximation (RPA) theories in taking the correlation effects into account. The Mathematical machinery of the SCR theory is rather complicated. The aim of these notes is to provide the required background. The problems with Stoner and RPA theory are discussed and the way in which the SCR theory rectifies those problems is also discussed.

It is a widely accepted view that COVID 19 is either transmitted via surface contamination or via close contact of an un-infected person with an infected person. Surface contamination usually happens when infected water droplets from exhalation/sneeze/cough of COVID sick person settle on nearby surfaces. To curb this, social distancing and good hand hygiene advise is advocated by World health Organization (WHO). We argue that COVID 19 coronovirus can also be airborne in a puff cloud loaded with infected droplets generated by COVID sick person. An elementary calculation shows that a $5~\mu m$ respiratory infected droplet can remain suspended for about 9.0 minutes and a $2~\mu m$ droplet can remain suspended for about an hour! And social distancing advise of 3 feet by WHO and 6 feet by CDC (Centers for Disease Control and Prevention) may not be sufficient in some circumstances as discussed in the text., Comment: 6 pages and 1 figure

In this article an overview of the historical development of the key ideas in the field of magnetism is presented. The presentation is semi-technical in nature.Starting by noting down important contribution of Greeks, William Gilbert, Coulomb, Poisson, Oersted, Ampere, Faraday, Maxwell, and Pierre Curie, we review early 20th century investigations by Paul Langevin and Pierre Weiss. The Langevin theory of paramagnetism and the Weiss theory of ferromagnetism were partly successful and real understanding of magnetism came with the advent of quantum mechanics. Van Vleck was the pioneer in applying quantum mechanics to the problem of magnetism and we discuss his main contributions: (1) his detailed quantum statistical mechanical study of magnetism of real gases; (2) his pointing out the importance of the crystal fields or ligand fields in the magnetic behavior of iron group salts (the ligand field theory); and (3) his many contributions to the elucidation of exchange interactions in d electron metals. Next, the pioneering contributions (but lesser known) of Dorfman are discussed. Then, in chronological order, the key contributions of Pauli, Heisenberg, and Landau are presented. Finally, we discuss a modern topic of quantum spin liquids., 15 pages, 1 figure. arXiv admin note: text overlap with arXiv:1807.11291

In a recent comment (arXiv:1906.05742) on the preprint (arXiv:1807.08572) entitled "Coexistence of Diamagnetism and Vanishingly Small Electrical Resistance at Ambient Temperature and Pressure in Nanostructures", it is pointed out that the reduction of the four-probe resistance ($R_{4P}$) to zero value is accompanied by a rise in the two probe resistance ($R_{2P}$) in the same temperature range. This curious correlation between $R_{4P}$ and $R_{2P}$ is said to be pointing towards a non-superconducting "conductance percolation" transition (rather than "percolating superconducting transition" as proposed in the revised version of arxiv:1807.08572). The explanation offered in preprint arXiv:1906.05742 is quite reasonable, but the author leaves open the question of giant diamagnetism. In this short comment I suggest a plausible cause of the giant diamagnetism found in nanostructures. It could be due to gapped electronic energy spectrum of nanoparticles which is due to quantum confinement effects, and that suppresses the electronic scattering mechanism leading to a very high value of Langevin diamagnetism., Comment: 5 pages, 1 figure

Related to the electronic structure of cuprate high-Tc superconductors there are two prevailing views: In one view, Pines and collaborators argue that cuprates consist of two electronic subsystems: one with localized spins and the other having itinerant character. Contrary to that, Phil Anderson has argued for one-component or one-band model for cuprates. Thus, a very natural question arrises: What is the actual electronic system in cuprates? Are these two-component or one-component systems? After a careful consideration of both the views, we argue in favor of one-component or Andersonian view. The key lies in the dual character of electrons in narrow d bands, and we put forward a semiclassical model using which we could quantitatively account for oxygen NMR shift data in $La_{2-x}Sr_xCuO_4$ within the single component view., Comment: 11 pages, 6 figures, comments will be appreciated

We comment on the electronic structure of Nickelate system $Nd Ni O_2$ which shows superconductivity on doping. The doped system $Nd_{0.8}Sr_{0.2}NiO_2$ shows (most probably unconventional) superconductivity with transition temperatures ranging from $9~K$ to $15~K$\cite{dang}. The resistivity of the parent compound $Nd NiO_2$ shows a minimum at around 60K, and an up-turn at lower temperatures. In the current understanding it is thought to be originating from a Kondo like coupling between mobile d-states of the $Nd~5d$ bands and un-paired electrons in $Ni 3d_{x^2-y^2}-O2p$ hybrid orbitals of $Ni^{1+}$ and $O^{2-}$ions. In this note we offer alternative possibilities of the observed resistance minimum in $LaNiO_2$. We attempt to construct a "road-map" of various possibilities to comprehend the observed behaviour and suggest further experiments to prove or disprove a given explanation. We also compare and contrast Nickelates with Cuprates. Comparison points towards unconventional superconductivity in Nickelates., Comment: 8 pages, 3 figures

A key point from the experiment related to the "noise" pattern in figure 3(a) of arXive:1807.08572 is that it is a function of temperature. We put forward a possible explanation. We argue that it is the elasto-magnetic coupling in which the diamagnetic surface currents on the surface of nanoparticles couple to surface phonon modes. As the temperature is increased (say from 210 K to 220 K), successive phonon modes are excited, one by one. This is due to quantum confinement where phonon modes take discrete values of energy (in bulk, the modes are quasi-continuous). One by one excitation of phonon modes modulates the surface currents on nano-particles that led to a fluctuating magnetization thus "noise" in the lower part of the susceptibility data where the system is in the superconducting state., 2 pages, no figure

Oscillatory effects in magnetic susceptibility of free electrons in a strong magnetic field is well known phenomenon and is well captured by Lifshitz-Kosevich formula. In this paper we point out similar oscillatory effects in Stoner susceptibility which makes the system to oscillate between paramagnetic phase and ferromagnetic phase alternatively as a function of external magnetic field strength. This effect can happen in a material which is tuned near to its magnetic instability. We suggest an experimental set-up to observe this effect. We also suggest that our result can be exploited to control a quantum critical system around its quantum critical point to study its thermodynamical or transport properties.

Air travel has become one of the most common means of transportation. The most common question which is generally asked is: How does an airplane gain lift? And the most common answer is via the Bernoulli principle. It turns out that it is wrongly applied in common explanations, and there are certain misconceptions. In an alternative explanation the push of air from below the wing is argued to be the lift generating force via Newton's law. There are problems with this explanation too. In this paper we try to clear these misconceptions, and the correct explanation, using the Lancaster-Prandtl circulation theory, is discussed. We argue that even the Lancaster-Prandtl theory at the zero angle of attack needs further insights. To this end, we put forward a theory which is applicable at zero angle of attack. A new length scale perpendicular to the lower surface of the wing is introduced and it turns out that the ratio of this length scale to the cord length of a wing is roughly $0.4930\pm0.09498$ for typical NACA airfoils that we analyzed. This invariance points to something fundamental. The idea of our theory is simple. The "squeezing" effect of the flow above the wing due to camber leads to an effective Venturi tube formation and leads to higher velocity over the upper surface of the wing and thereby reducing pressure according the Bernoulli theorem and generating lift. Thus at zero angle of attack there is no need to invoke vortex and anti-vortex pair generation. In fact vortex and anti-vortex pair generation cannot be justified. We come up with the equation for the lift coefficient at zero angle of attack: \[C_l = \frac{1}{c}\int_0^c dx \left(\frac{h_c^2}{(h_c - f(x))^2}-1\right).\] Here $C_l$ is the lift coefficient, $h_c$ is our new length scale perpendicular to the lower surface of the wing and $f(x)$ is the functional profile of the upper surface of the wing., Comment: 9 pages, 5 figures

An introduction to the Zwanzig-Mori-G\"{o}tze-W\"{o}lfle memory function formalism (or generalized Drude formalism) is presented. This formalism is used extensively in analyzing the experimentally obtained optical conductivity of strongly correlated systems like cuprates and Iron based superconductors etc. For a broader perspective both the generalised Langevin equation approach and the projection operator approach for the memory function formalism are given. The G\"{o}tze-W\"{o}lfle perturbative expansion of memory function is presented and its application to the computation of the dynamical conductivity of metals is also reviewd. This review of the formalism contains all the mathematical details for pedagogical purposes., Comment: 17 pages; 2 figures and 2 tables

The Kelvin Water Dropper was discovered by Lord Kelvin in 1867 and it works on the principle of electrostatic induction. A working model of Kelvin Water Dropper is fabricated in the workshop facility of Physical Research Laboratory, Ahmedabad. We, for the first time, performed a quantitative measurement of the temporal development of charge using a new method that we call "Effective Capacitance method". With this, the Kelvin Water Dropper experiment can be introduced in undergraduate curriculum, where students can perform quantitative measurements with the apparatus using our "Effective Capacitance method". This should change the generally held view of Kelvin water dropper as being an entertaining toy to a mature educational device., 10 pages, 8 figures

We report a comparative study of the scattering rates using different formalisms such as Allen\cite{allen_71}, Shulga et al.\cite{shulga_91}, Mitrovi�� et al.\cite{mitrovic_85}, Sharapov et al\cite{sharapov_05} and memory function formalism\cite{mori_65}. We discuss the frequency and the temperature dependent scattering rates for the case of electron-phonon interactions in these formalisms. The analysis has been done for different forms of phonon density of states (PDOS) and electron density of states (EDOS). An advantage of our study is that it shed light on the physical assumptions used in these formalisms. From this detailed comparison, we observe that the memory function formalism is the most general one. All other formalisms are based on restrictive assumptions as discussed in this work., 13 pages, 7 figures

For graphene (a Dirac material) it has been theoretically predicted and experimentally observed that DC resistivity is proportional to $ T^4$ when the temperature is much less than Bloch- Gr\"{u}neisen ($\Theta_{BG}$) temperature and T linear in opposite case ($T>>\Theta_{BG}$). Going beyond the DC case, we investigate the dynamical conductivity in graphene using the powerful method of memory function formalism. In the DC (zero frequency regime) limit, we obtained the above mention behavior which was previously obtained using the Bloch-Boltzmann kinetic equation. In the finite frequency regime, we obtained several new results: (1) the generalized Drude scattering rate, in the zero temperature limit, shows $\omega^4 $ behavior at low frequencies ($\omega << k_B \Theta_{BG}/ \hbar$) and saturates at higher frequencies. We also observed the Holstein Mechanism, however, with different power laws from that in the case of metals; (2) At higher frequencies, $\omega>>k_B \Theta_{BG}/ \hbar$, and higher temperatures $T>>\Theta_{BG}$, we observed that the generalized Drude scattering rate is linear in temperature. In addition, several other results are also obtained. With the experimental advancement of this field, these results should be experimentally tested., Comment: 8 pages, 4 figures, 1 table

We consider non-equilibrium relaxation of electrons due to their coupling with phonons in a simple metal. In our model electrons are living at a higher temperature than that of the phonon bath, mimicking a non-equilibrium steady state situation. We study the relaxation of such hot electrons proposing a suitable generalization of the memory function formalism formulated by G��tze and W��lfle[Phys. Rev. B 6, 1226 (1972)]. We derive analytical expressions for both dc and optical scattering rates in various temperature and frequency regimes. Limiting cases are in accord with the previous studies. An interesting feature, that the dc scattering rate at high temperatures and optical scattering rate at high frequencies, are independent of the temperature difference between the electrons and the phonons is found in this study. The present formalism forms a basis which can also be extended to study hot-electron relaxation in more complex situations, 11 pages, 4 figures, 1 table, Revised Version

An attempt is made to de-mystify the apparent "paradox" between microscopic time revsersibility and macroscopic time irreversibility. It is our common experience that a hot cup of coffee cools down to room temperature and it never automatically becomes hot (unless we put that in a microwave for heating or on stove etc) and there are numerous examples. This "one sidedness" of physical processes (like cooling of hot cup) is in apparent contradiction with the time reversibility of the dynamical equations of motion (classical or quantum). The process of automatic heating of a cold cup etc is perfectly possible from the dynamical equations perspective. Ludwig Boltzmann explained this "one sidedness" of physical processes starting from dynamical equations (his H-theorem). A criticism was raised by Boltzmann's contemporaries. The origin of this criticism lies in the very philosophy of "mechanism" that was very prevalent in the 19th century. Everyone wanted to understand physical phenomena through Newtonian mechanics (even J. C. Maxwell devised a mechanical mechanism using gears to explain the electromagnetic field!). The central issue was how can one obtain this "one sidedness" (time irreversiblility) if the underlying dynamical laws are time reversible. Number of articles exist in literature on the issue. But those are mathematically oriented and a simple presentation from practical point of view is seriously lacking. This article is an attempt to de-mystify this "paradox" from simple and practical point of view., 6 pages, 3 figures. Based on a talk given at the conference "Mind, Matter, and Mathematics--a dialogue" at New Tehri, Uttakhand, India, on 12th-14th March, 2014

It is well known that mean-field theories fail to reproduce the experimentally known critical exponents. The traditional argument which explain this failure of mean-field theories near a critical point is the Ginsburg criterion in which diverging fluctuations of the order parameter is the root cause. We argue, contrary to the above mentioned traditional view, that diverging fluctuations in real physical systems near a critical point are genuine consequence of the breakdown of the property of statistical independence, and are faithfully reproduced by the mean-field theory. By looking at the problem from the point of view of "statistical independence" the divergence of fluctuations in real physical systems near criticality becomes immediately apparent as a connection can be established between diverging correlation length and diverging fluctuations. To address the question of why mean-field theories, much successful qualitatively, fail to reproduce the known values of critical indices we argue, using the essential ideas of the Wilsonian renormalization group, that mean-field theories fail to capture the long length scale averages of an order parameter near a critical point., 6 pages; 1 figure

We have studied the temperature dependence of the rate of energy transfer from electronic sub-system to phononic sub-system in the case of cuprates, when the system is photo-excited by a femtosecond laser pulse. In the pseudogap state, taking the electronic dispersion {\it as linear} near the nodal points of the Brillouin zone, we show that the rate of energy transfer from electronic sub-system to phononic sub-system is proportional to $T^{5}$ at lower temperatures ($T<>T_0$), here $T_0$ is the Debye temperature for cuprates. The linear electronic dispersion in the pseudogap state introduces new terms in the expression of energy transfer as given by M. I. KAGANOV et.al. \cite{kaganov}. {\it But the leading terms are the same which are found in the case of metals in the above reference.} The electron-phonon relaxation time follows $T^{-3}$ law for cuprates which agrees well with the experimental results \cite{demsar,Jdemsar}., Comment: 18 pages, 10 figures

While analyzing second order thermodynamical phase transitions, Lev Landau (the famous Russian physicist) introduced a very vital concept, the concept of an "order parameter". This not only amalgamated the previous fragmentary theoretical understanding of phase transitions (an arsenal of mean-field theories) but also it put forward the important theory of "spontaneous symmetry breaking". Today, order parameter concept is a paradigm both in condensed matter physics and in high energy physics, and Landau theory is a pinnacle of all mean-field theories. Mean field theories are good qualitative descriptors of the phase transition behavior. But all mean-field theories (including Landau's theory) fail at the critical point (the problem of large correlation length). The problems with large correlation length in quantum many-body systems are the hardest problems known in theoretical physics (both in condensed matter and in particle physics). It was Ken Wilson's physical insights and his powerful mathematical skills that opened a way to the solution of such hard problems. This manuscript is a perspective on these issues. Starting with simple examples of phase transitions (like ice/water; diamond/graphite etc.) we address the following important questions: Why does non-analyticity (sharp phase transitions) arise when thermodynamical functions (i.e., free energies etc) are good analytic functions? How does Landau's program unify all the previous mean-field theories? Why do all the mean-field theories fail near the critical point? How does Wilson's program go beyond all the mean-field theories? What is the origin emergence and universality?, Comment: 30 Pages, 19 figures

A toy model is developed to capture "dance of pre-formed pairs" in the pseudogap state of high temperature cuprate superconductors. The model is a crude description of a hypothetical situation in which spin-driven spatial organization of the pre-formed pairs is analyzed. Within a mean-field theory (a slight generalization of Bragg-Williams theory) we examined the behaviour of heat capacity and an "order parameter" which captures the short range correlations between the pre-formed pairs. Below a transition temperature these short range correlations enhance and leads to a long range order (spin-density wave). This is examined through the breakdown of statistical independence., Comment: 6 pages, 13 figures

We theoretically investigate charge dynamics in weakly coupled $CuO_2$ planes of the cuprate $Ca_{2-x} Na_x Cu O_2 Cl_2$ (CNCOC) using Kubo formula for optical conductivity in the underdoped regime. The spectral function needed in Kubo formula is obtained from an analytical form of electron Green's function proposed (ansatz) by Yang-Rice-Zhang (YRZ) for the underdoped cuprates based on their previous renormalized mean field theory and on the investigations of weakly coupled Hubbard ladders. Although to an unaided eye the results of the numerical calculation look very similar to that found experimentally in [K. Waku etal. 2004] but a careful examination with extended Drude formalism shows that YRZ ansatz for the calculation of optical conductivity is not sufficient to understand the charge dynamics in $CuO_2$ planes of the cuprate CNCOC. More physics is needed especially electromagnetic response from bound charges., 8 pages and 21 figures

The present review is devoted to our recent studies on the excitonic motion in photosynthetic systems. In photosynthesis, the light photon is absorbed to create an exciton in the antenna complex of the photosynthetic pigments. This exciton then migrates along the chain-biomolecules, like FMO complex, to the reaction centre where it initiates the chemical reactions leading to biomass generation. Recently, it has been experimentally observed that the exciton motion is highly quantum mechanical in nature i.e., it involve long time ($\sim 600$ femto sec) quantum coherence effects. Traditional semiclassical theories like Forrester's and second Born master equations cannot be applied. We point out why the 2nd Born non-Markovian master equation and its Markovian limit (also called the Redfield master equation) cannot be used to explain the observed long coherences. Briefly, the reason is that these approaches are perturbative in nature and in real light harvesting systems various couplings (system-system and system-bath) are of the similar order of magnitude. Various new approaches are being developed to go beyond the above two limiting theories. The present review is not a review in the usual sense of the word as we summarize our own approaches and only refer to the literature for the other ones. A brief introduction to the sophisticated 2D photon echo spectroscopy is also given at the end with an emphasis on the underlying physics of the multidimensional echo spectroscopies., 32 pages; invited article for multi-author theme issue: "Photosynthesis: Quantum Coherence and Entanglement" (Open Academic Press)

We propose a simple stochastic model which successfully explains the long coherence effects observed in photosynthetic Excitation Energy Transport (EET) by 2D photon echo experiments of G. S. Engel et. al. (Nature, {\bf 446} 782, (2007)). Our Two-Component Phonon Spectrum (TCPS) model is based upon the division of phonon degrees of freedom into a systematic component which is treated through polaron transformation and a stochastic component which is treated through dynamical disorder. This model successfully explains the observed long coherence upto $ \sim 600 fsec$ in EET experiments., Comment: 5 pages and 14 figures; This paper has been withdrawn by the authors

A direct numerical algorithm for solving the time-nonlocal non-Markovian master equation in the second Born approximation is introduced and the range of utility of this approximation, and of the Markov approximation, is analyzed for the traditional dimer system that models excitation energy transfer in photosynthesis. Specifically, the coupled integro-differential equations for the reduced density matrix are solved by an efficient auxiliary function method in both the energy and site representations. In addition to giving exact results to this order, the approach allows us to computationally assess the range of the reorganization energy and decay rates of the phonon auto-correlation function for which the Markovian Redfield theory and the second order approximation is valid. For example, the use of Redfield theory for $\lambda> 10 \textrm{cm}^{-1}$ in systems like Fenna-Mathews-Olson (FMO) type systems is shown to be in error. In addition, analytic inequalities are obtained for the regime of validity of the Markov approximation in cases of weak and strong resonance coupling, allowing for a quick determination of the utility of the Markovian dynamics in parameter regions. Finally, results for the evolution of states in a dimer system, with and without initial coherence, are compared in order to assess the role of initial coherences., Comment: 24 pages and 38 figures

As the title says we want to answer the question; how and why does statistical mechanics work? As we know from the most used prescription of Gibbs we calculate the phase space averages of dynamical quantities and we find that these phase averages agree very well with experiments. Clearly actual experiments are not done on a hypothetical ensemble they are done on the actual system in the laboratory and these experiments take a finite amount of time. Thus it is usually argued that actual measurements are time averages and they are equal to phase averages due to ergodicity. Aim of the present review is to show that ergodicity is not relevant for equilibrium statistical mechanics (with Tolman and Landau). We will see that the solution of the problem is in the very peculiar nature of the macroscopic observables and with the very large number of the degrees of freedom involved in macroscopic systems as first pointed out by Khinchin. Similar arguments are used by Landau based upon the approximate property of "Statistical Independence". We review these ideas in detail and in some cases present a critique. We review the role of chaos (classical and quantum) where it is important and where it is not important. We criticise the ideas of E. T. Jaynes who says that the ergodic problem is conceptual one and is related to the very concept of ensemble itself which is a by-product of frequency theory of probability, and the ergodic problem becomes irrelevant when the probabilities of various micro-states are interpreted with Laplace-Bernoulli theory of Probability (Bayesian viewpoint). In the end we critically review various quantum approaches (quantum-statistical typicality approaches) to the foundations of statistical mechanics., Comment: 17 pages, 8 figures, Review Paper (prepared for Rev. Mod. Phys.); substantial changes and additions in the last section

The present paper is a review of the phenomena related to non-equilibrium electron relaxation in bulk and nano-scale metallic samples. The workable Two-Temperature Model (TTM) based on Boltzmann-Bloch-Peierls (BBP) kinetic equation has been applied to study the ultra-fast(femto-second) electronic relaxation in various metallic systems. The advent of new ultra-fast (femto-second) laser technology and pump-probe spectroscopy has produced wealth of new results for micro and nano-scale electronic technology. The aim of this paper is to clarify the TTM, conditions of its validity and non-validity, its modifications for nano-systems, to sum-up the progress, and to point out open problems in this field. We also give a phenomenological integro-differential equation for the kinetics of non-degenerate electrons that goes beyond the TTM., Comment: 12 pages,2 figures, major revision

The Two Temperature model of M I Kaganov, I M Lifshitz and L V Tanatarov (Sov. Phys. JETP 4, 173 (1957)) about relaxation between electrons and bulk phonons is extended to the case of surface phonons. The state of electrons and phonons is described by equilibrium Fermi and Bose functions with different temperatures. The new feature added is the geometric constraint of surface phonons. We obtain expressions for the energy transfer rate from degenerate hot electrons to surface-phonons, which is order of magnitude less than that for the bulk., 4 pages, 1 figure

A model calculation is given for the energy relaxation of a non-equilibrium distribution of hot electrons prepared in a metallic sample that has been subjected to homogeneous photo-excitation by a femtosecond laser pulse. The model assumes that the delta pulse photoexcitation creates two interpenetrating electronic subsystems, initially comprising a dilute energy-wise higher-lying non-degenerate hot electron subsystem, and a relatively dense, lower-lying electron subsystem which is degenerate. In the femtosecond time regime the relaxation process is taken to be dominated by the electron-(multi) phonon interaction, resulting in a quasi-continuous electron energy loss to the phonon bath. The kinetic model is given for this time regime, beacuse in this time regime the usual Two Temperature model is not applicable. The Two Temperature model assumes that the hot electrons and phonons are in their respective equilibrium states (Fermi and Bose) but at a different temperatures. One uses the Bloch-Boltzmann-Peierls transport formula to calculate the energy transfer rate. In the present Kinetic model a novel physical feature of slowing down (due to Fermionic blocking of interaction phase space) of electron-phonon relaxation mechanism near the Fermi energy of degenerate electronic subsystem is considered. This leads to a peaking of the calculated hot electron distribution at the Fermi energy. This feature, as well as the entire evolution of the hot electron distribution, may be time-resolved by a femto-second pump-probe study., Comment: 5 pages,4 figures