This paper has developed a phenomenological approach to evaluation of the Landau parameters in d- wave superconductors with anisotropic **Fermi** surfaces and energy gaps. As we have emphasized, **Fermi** **liquid** theory cannot provide to give an adequate description of the normal state properties of the high- T c superconductors. Thus, we restricted our calculations well below the critical temperature T c that will be considered as being possibly explicable in terms of **Fermi** **liquid** theory [22]. The symmetry of the square lattice restricts the form of expansion of the interaction function to more Landau parameters. As the case for **Fermi** **liquid** in normal and superfluid 3 He [23,24], we

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The mean-field approximation (Walecka model) to the theory of QHD produces a thermodynamically consis- tent field theoretical approximation. One can directly show that dynamical single particle energy defined in Green’s function and quasiparticle energy defined by Landau’s fundamental requirement are equal, and conse- quently, **Fermi** **liquid** properties of nuclear matter are discussed consistently at zero temperature [34]-[36]. The self-consistency, equality of dynamical and quasiparticle single particle energies, can be proved only if nonli- near interactions are properly renormalized. The fundamental requirement of conserving approximation or DFT is satisfied. The nonlinear (σ, ω) effective model is a conserving approximation [37] [38], which is also essential for self-consistent finite temperature approximations. Nonlinear interactions should be properly renormalized as effective masses and effective coupling constants to be a conserving approximation.

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properties display universal behavior 7 . Experimental works 8-13 have indicated that several heavy-electron compounds and related alloys ( particularly f-electron alloys)display non- **Fermi** **liquid** behavior. Typically, the non –**Fermi** **liquid** behavior is observed as a diverging linear coefficient of specific-heat C for temperature T =0. There is strong T dependence of the magnetic susceptibility χ as T =0. The electrical resistivity ρ shows a peculiar T dependence (ρ = A T m having A > 0 and m =1 instead of the **Fermi** –**liquid** behavior m=2) In this paper, we have studied optical properties of some non –**Fermi** **liquid** alloys. Generally, optical investigations extending over a broad frequency range and at various temperatures are an efficient experimental tool for the simultaneous study of the energy and temperature of intrinsic parameter characterizing the systems. Of particular relevance in connection with the anomalous dc electrical resistivity, is the identification of energy and temperature dependence of the relaxation time .

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Furthermore it is observed that the ground state close to QCP in many heavy fermion systems is superconducting in which the superconducting pairing mechanism is different from conventional phonon mediated. It is commonly believed that the unconventional superconducting pairing mechanism is electronic in origin. The question is why such an unconventional pairing mechanism is operative only close to QCP and not far away from it? We attempt to explain this in the following way. It is well known that every electronic system has a tendency to form a bosonic ground state in order to reduce its energy since bosons can condense into the same state at low temperatures whereas the fermions cannot do so due to Pauli’s exclusion principle. It is due to this tendency that superconducting ground states are formed in case of certain metallic systems. However one needs a suitable mechanism to form superconducting Cooper pairs (bosons) out of electrons (fermions) in order to realize the superconducting ground state. We claim that the unconventional pairing mechanism is a consequence of the fact that the valence electrons for systems close to QCP are not fermionic in nature. Therefore the tendency to form a bosonic ground state in the valence electronic system is supported in such a case and superconductivity emerges. Far away from QCP (but close to 0K) the valence electrons are fermions and hence the unconventional pairing mechanism is not supported in such a case. Since **Fermi** **liquid** theory does not hold close to QCP, quasi-particles do not form and therefore it is possible that the itinerant valence electrons find a glue to bind themselves together into a Cooper pair. Analogous to the case of phonon mediated superconductors where the glue is provided by the electron phonon coupling which causes an effective attractive interaction between two electrons giving rise to Cooper pairs [21, 22], the glue in case of heavy fermion superconductors seems to be generated by the temperature dependent attractive interaction between 4f and itinerant valence electron – Note that Kondo effect is an example of asymptotic freedom [23, 24] in condensed matter in which the strength of attractive coupling between 4f and valence electron is temperature dependent. The strength of this coupling increases with reducing temperature (see Supplementary Information Section C). This coupling is a result of hybridization between 4f and valence electron. An effect of such temperature dependent coupling is clearly visible in the photoemission spectra as demonstrated in our earlier publication [25] – effectively giving rise to an attractive interaction between two itinerant valence electrons binding them into a Cooper pair.

point in momentum space, whereas fermionic properties are determined by gapless excitations along the entire **Fermi** surface, a manifold with codimension 1, a discrepancy that is hard to deal with in momentum-based RG schemes. For these reasons, and following Maier and Strack [21], we use a frequency cutoff, which allows us to capture the soft-mode excitations as they become singular toward q = 0.

The distinction between an instability to ferromagnetism and an instability to antiferromagnetism is an important one. For incipient antiferromagnets, the magnetic fluctua- tions are peaked at some nonzero wave vector Q, and scatter the electrons between certain “ hot spots ” on the **Fermi** surface. In this Letter, however, we address the ferromagnetic case; furthermore, we work in two spatial dimensions, in which this is a strong-coupling problem. Because the instability is ferromagnetic, the magnetic fluctuations are peaked at Q ¼ 0 , which implies strong forward scattering at every point on the **Fermi** surface. Nonetheless, the induced correlations between the fermions are strongest between points on the **Fermi** surface which have a common tangent. These regions, known as “ patches, ” are often (though not in this Letter) the only parts of the **Fermi** surface that are retained in theories of ferromagnetic quantum criticality [5 – 10].

It has been recently shown that the behavior of quantum liquids in the ultrarelativistic regime is very diﬀerent from the normal **Fermi** **liquid** (FL) behavior. This diﬀerence of behavior has recently been exposed both in the context of quantum electrodynamics (QED) and quantum chromodynam- ics (QCD)[1, 2]. It might be mentioned here that for the case of non-relativistic (NR) plasma, the magnetic interaction is supressed in powers of (v/c) 2 and hence can be neglected. For the case of

Light amplification by stimulated emission of radiation, well-known for revolutionising photonic science, has been realised primarily in fermionic systems including widely applied diode lasers. The prerequisite for fermionic lasing is the inversion of electronic population, which governs the lasing threshold. More recently, bosonic lasers have also been developed based on Bose-Einstein condensates of exciton-polaritons in semiconductor microcavities. These electrically neutral bosons coexist with charged electrons and holes. In the presence of magnetic fields, the charged particles are bound to their cyclotron orbits, while the neutral exciton-polaritons move freely. We demonstrate how magnetic fields affect dramatically the phase diagram of mixed Bose-**Fermi** systems, switching between fermionic lasing, incoherent emission and bosonic lasing regimes in planar and pillar microcavities with optical and electrical pumping. We collected and analyzed the data taken on pillar and planar microcavity structures at continuous wave and pulsed optical excitation as well as injecting electrons and holes electronically. Our results evidence the transition from a Bose gas to a **Fermi** **liquid** mediated by magnetic fields and light-matter coupling.

Certain electronic states occur universally, and across a great number of systems with different chemistries. A prominent example is that of the Lan- dau **Fermi** **liquid**. This phenomenological theory makes robust predictions, and is found to be valid in materials ranging from nearly-free electron sys- tems to ‘heavy fermion’ metals where interactions are strong. However, there are cases where the **Fermi** **liquid** description breaks down [3], particularly in strongly correlated systems [4], a subject of much topical interest. One such case is found when a system is tuned to proximity to a quantum critical point [5], frequently accompanied by the formation of a phase of lowered symmetry. This may result in superconductivity, or in one of a wide variety of orientationally and translationally ordered states that has been proposed [6].

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As the forward scattering interactions become fixed points, the physics that they describe becomes Landau’s **Fermi** **liquid** theory [1, 2]. While the original particles in the microscopic models may be strongly interacting, the elementary fermionic exci- tations of the **Fermi** **liquid** are interacting only weakly and most of their properties resemble those of the degenerated **Fermi** gas (at temperature T = 0). The terms that would lead to the finite lifetime of these quasiparticles turn out to be irrele- vant, therefore, the quasiparticles have essentially infinite lifetime. As Landau was describing his theory himself, if you very slowly (“adiabatically”) turn off the strong interactions in the original model, you will arrive at the description that still cor- rectly predicts many of the macroscopic properties of the system. The nonforward scattering interactions have to be small and irrelevant in Landau’s theory and they are being ignored. The forward scattering interaction is called Landau parameter and it is the only interaction in the **Fermi** **liquid** theory.

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Deep inelastic lepton-nucleus scattering has shown that bound nucleons structure functions are different from free nucleons structure functions [1-5]. This phenomenon has been known as the EMC (European Muon Collaboration) effect [5]. This effect declared that the distribution function of quarks in the bound nucleons inside nuclei is different from free nucleons. The binding energy and the **Fermi** mo- tion of nucleon inside nuclei have important role in the EMC effect in medium and large x ranges. Considering these effects could not explain bound nucleons structure functions and the EMC effect in all ranges. There are other effects such as pion cloud, shadowing, quark ex- change, ∆ particle, and so on, which should be considered to explain nucleons structure functions and the EMC effect. Because quark distribution functions inside nuclei are af- fected by nuclear environment, bound nucleons structure are different from free nucleons structure. As a result, con- sidering these nuclear effects could improve the extracted results. Nucleons inside nuclei are surrounded by pion cloud, so for achieving precise bound nucleons structure functions and the EMC effect, it seems that considering pionic contribution could improve theoretical results. Therefore, the probability of an incident virtual photon in- teracts with a nucleon is decreasing and this virtual photon is interacting with Pion cloud around nucleon inside nuclei.

High-resolution angle-resolved photoelectron spectroscopic measurements were made of the **Fermi** edge of a single crystal of Bi2Sr2CaCu2O8 at 90 K along several directions in the Brillouin zone. The resultant **Fermi**- level crossings are consistent with local-density band calculations, including a point calculated to be of Bi-O character. Additional measurements were made where bands crossed the **Fermi** level between 100 and 250 K, along with measurements on an adjacent Pt foil. The **Fermi** edges of both materials agree to within the noise. Below the **Fermi** level the spectra show correlation effects in the form of an increased effective mass, but the essence of the single-particle band structure is retained. The shape of the spectra can be explained by a lifetime-broadened photohole and secondary electrons. The effective inverse photohole lifetime is linear in energy.

clearly resolved on top of the rather weak background originating from the HOPG π -band. This is consistent with a UP spectroscopy report on a 7.5 nm thick ClB-SubPc ﬁ lm on Si. 51 Further, peaks are observed at higher binding energies. In contrast, on Cu(111) only weak and broad features are visible between 0 and − 2 eV. These stem primarily from the Cu d- band He(I) β satellite features at − 0.8 eV. Additional contributions from the remainder of the Cu(111) Shockley surface state ( − 0.2 to − 0.4 eV) and from a partially ﬁ lled lowest unoccupied molecular orbital near the **Fermi** edge are expected at the positions indicated in Figure 3 following the two-photon photoemission data in ref 21. Below − 2 eV, the Cu d-bands manifest as the strongest features in the ClB-SubPc/ Cu(111) UP spectrum. Their broad structure is indicative of Figure 2. Structure of the ClB-SubPc molecule (a) before and (b)

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The superfluid phase of strongly interacting fermions is distinguished from the normal phase by spontaneous breaking of gauge symmetry. Other phases of matter, including those studied in the context of the fractional quantum Hall effect and certain spin liquids, cannot be distinguished by broken symmetries but rather by their topological order [37, 38]. The discovery of topological insulators spurred interest in topological phases that do not break time-reversal symmetry [39–42]. Such phases can be realized in lower dimensional **Fermi** gases with strong spin-orbit coupling in the presence of Zeeman fields. In a non-interacting 2D gas, a non-Abelian spin-orbit gauge field gives rise to topological insulators with protected edge states. Interactions lead to much richer physics; even for purely contact interactions, spin-orbit coupling gives rise to effective p-wave interactions, resulting in topological superfluids that host Majorana fermions at the interface to topologically trivial phases [43, 44].

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of DC magnetic fields up to 45 T, from which a monotonic smooth background has been subtracted. Quantum oscillations periodic in inverse magnetic field are observed for magnetic field tilt angles θ spanning [001], [111] to [110] crystal directions, and extending down to magnetic fields at least as low as 22 T. An example Fourier transform of quantum oscillations in inverse magnetic field shown in figure 2(c) reveals multiple quantum oscillation frequencies between 300 − 1500 T. The quantum oscillation frequency >1 kT is seen most clearly in the high magnetic field range (figure 2(c) inset). While this higher quantum oscillation frequency is close to a harmonic of lower frequency quantum oscillations, there is no obvious observation of frequencies corresponding to harmonics of dominant amplitude low frequency quantum oscillations. The temperature dependence of the measured quantum oscillation amplitude follows a Lifshitz-Kosevich (LK) form, yielding cyclotron effective masses of m ∗ /m e between 3 − 10 for the various measured quantum oscillation frequencies (figure 2(d), [19, 20]). Figure 2(b) shows the angular dependence of the measured quantum oscillation frequencies for magnetic field tilt angles spanning [001], [111] to [110] crystal directions, which reveals only a subtle variation in quantum oscillation frequency as a function of angle, consistent with a three-dimensional **Fermi** surface geometry.

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In this paper, we will generalize this construction to allow an arbitrary number of arbitrary subspaces, rather than just a timelike geodesic and the perpendicular space, and an arbitrary number d of dimensions. In Sec. II we will construct the generalized coordinate system, in Sec. III we compute the connection, and in Sec. IV we compute the metric in the generalized **Fermi** coordinates. We conclude in Sec. V.

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− 1) in this version of the dissipative **Fermi**-Ulam model. Figure 1(a) shows the results for α = 0.93 and ǫ = 0.04. The two branches of the unstable manifold evolve as follows: the upward branch generates the attracting fixed point while the downward branch generates the chaotic attractor. The two branches of the stable manifold establish boundaries for both the chaotic and fixed point attractors (the details of the corresponding basin boundaries are shown in figure 2(b)). Increasing the value of the control parameter α, which is equivalent to reducing the strength of the dissipation, causes a homoclinic orbit to be generated at α ≈ 0.93624 . . .. Since the two branches of the stable manifold establish the edges of the basin boundaries, the generation of the homoclinic orbit also results in a collision of the chaotic attractor with the border of its basin boundary. Such a collision is often called a boundary crisis [24, 25, 27]. Simultaneously, the chaotic attractor and its basin of attraction are destroyed. Figure 1(b) shows the stable and unstable manifolds for the control parameters ǫ = 0.04 and α = 0.9375 immediately after the boundary crisis. The birth of the homoclinic orbit is clearly evident.

It clearly seen in Fig. 4.5a,b there is a broadening and decaying pulse moving down the chain reaching the end in less than 300 time units (=3 ps). The pulse can be observed m ost distinctly in the NH stretch energies. W hile energy is efficiently transferred out o f the initially excited NH stretch into the amide modes on molecule six, this energy is not transferred with the same efficiency out o f the amide modes across the hydrogen bond to molecule five. The involvement o f the Amide-II mode in the stretch- wag **Fermi** resonance is crucial here as it appears to sequester a quarter o f the available energy in the initial decay o f the excited NH. The Amide-II modes have little amplitude on the CO stretch, and so have little capacity to transfer energy by this means. Because of this, more than 30% o f the energy remains in the initially excited molecule while only about 10% remains in the initially excited NH oscillator. The energy in the Amide-II mode would account for about two thirds of the energy in the initially excited molecule at long times. The other feature worth noting is the small reflection o f energy back into the initially excited stretch which causes a small secondary pulse to start down the chain giving the two peaked appearance to the energy in the fifth molecule. Varying cmco from -5.0 to -7.5 aJ/Ä 3 produced very little change in the efficiency or speed o f the energy transfer.

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In this work, we introduce the classification of subclasses of blazars and an empirical function of peak frequency estimation using effective spectral indexes, investigate the correlation between effective radio to X-ray spectral index and peak frequency, the correlations between peak/integrate luminosity and γ-ray/optical luminosity. Following conclusions can be come to: 1. There are only 3 subclasses (LSPs, ISPs, and HSPs) for **Fermi** blazars, and there is no extreme high peak frequency component for blazars; 2. There is an anti-correlation between effective spectral index (α rx ) and peak

Data of sources could be downloaded from the website of LAT Monitored Source List Light Curves. Commonly, Fluxes of **Fermi** source is highly variable. Here, F ( t ) denotes the flux at time t. Because the time interval of the flux F(t) is one day, the daily variable intensity of flux could be calculated by the formula