Abstract:
We study elementary low energy excitations inside a supersolid. We find that the coupling between the longitudinal lattice vibration mode and the superfluid mode leads to two longitudinal modes (one upper branch and one lower branch) inside the supersolid, while the transverse modes in the supersolid stay the same as those inside a normal solid. We also work out various experimental signatures of these novel elementary excitations by evaluating the Debye-Waller factor, density-density correlation, vortex loop-vertex loop interactions, specific heat and excess entropy from the vacancies per mole.

Abstract:
We clarify elementary excitations in the $\Delta$-chain. They are found to be `kink'-`antikink' type domain wall excitations to the dimer singlet ground state. The characters of a kink and an antikink are quite different in this system: a kink has no excitation energy and is localized, while an antikink has a finite excitation energy and propagates. The excitation energy of a kink-antikink pair consists of a finite energy gap and a kinetic energy due to the free motion of the antikink. Variational wave functions for an antikink are studied to clarify its propagating states. All the numerical results are explained consistently based on this picture. At finite temperatures, thermally excited antikinks are moving in regions bounded by localized kinks. The origin of the low-temperature peak in the specific heat reported previously is explained and the peak position in the thermodynamic limit is estimated.

Abstract:
The elementary excitations of vibration in solids are phonons. But in liquids phonons are extremely short-lived and marginalized. In this letter through classical and ab-initio molecular dynamics simulations of the liquid state of various metallic systems we show that different excitations, the local configurational excitations in the atomic connectivity network, are the elementary excitations in high temperature metallic liquids. We also demonstrate that the competition between the configurational excitations and phonons determines the so-called crossover phenomenon in liquids. These discoveries open the way to the explanation of various complex phenomena in liquids, such as fragility and the rapid increase in viscosity toward the glass transition, in terms of these excitations.

Abstract:
It is shown that elementary excitations in fractal media obey the so-called parastatistics of a variable order. We show that the order of the parastatistics $N(k) $ is a function of wave numbers $k$ which depends on the fractal dimension $D$ as $N(k) \sim k^{D-3}$ and represents a specific characteristic of such media. This function $N(k)$ defines properties of the ground state for excitations and the behavior of the spectrum of thermal fluctuations. In particular, in fractal media fluctuations of the density acquire an amplification by the factor $N(\omega) \sim \omega ^{D-3}$ which can be related to the origin of $1/f$-noise.

Abstract:
We present a theory of the elementary spin excitations in transition metal ferromagnet nanoparticles which achieves a unified and consistent quantum description of both collective and quasiparticle physics. The theory starts by recognizing the essential role played by spin-orbit interactions in determining the energies of ferromagnetic resonances in the collective excitation spectrum and the strength of their coupling to low-energy particle-hole excitations. We argue that a crossover between Landau-damped ferromagnetic resonance and pure-state collective magnetic excitations occurs as the number of atoms in typical transition metal ferromagnet nanoparticles drops below approximately $10^4$, approximately where the single-particle level spacing, $\delta$, becomes larger than, $\sqrt{\alpha} E_{\rm res}$, where $E_{\rm res}$ is the ferromagnetic resonance frequency and $\alpha$ is the Gilbert damping parameter. We illustrate our ideas by studying the properties of semi-realistic model Hamiltonians, which we solve numerically for nanoparticles containing several hundred atoms. For small nanoparticles, we find one isolated ferromagnetic resonance collective mode below the lowest particle-hole excitation energy, at $E_{\rm res} \approx 0.1$ meV. The spectral weight of this pure excitation nearly exhausts the transverse dynamical susceptibility spectral weight. As $\delta$ approaches $\sqrt{\alpha} E_{\rm res}$, the ferromagnetic collective excitation is more likely to couple strongly with discrete particle-hole excitations. In this regime the distinction between the two types of excitations blurs. We discuss the significance of this picture for the interpretation of recent single-electron tunneling experiments.

Abstract:
We summarize previous works on the exact ground state and the elementary excitations of the exactly solvable BCS model in the canonical ensemble. The BCS model is solved by Richardson equations, and, in the large coupling limit, by Gaudin equations. The relationship between this two kinds of solutions are used to classiffy the excitations.

Abstract:
We propose a natural expansion of the atomic field operator in studying elementary excitations in trapped Bose-Einstein Condensation (BEC) system near T=0K. Based on this expansion, a system of coupled equations for elementary excitations, which is equivalent to the standard linearized GP equation, is given to describe the collective excitation of BEC in a natual way. Applications of the new formalism to the homogeneous case emphasize on the zero mode and its relevant ground state of BEC.

Abstract:
Possible types of elementary excitations in the symmetric spin-orbital model on the a square lattice are analyzed using a spherically symmetric self-consistent approach. The excitation spectra are calculated. The behavior of the corresponding correlation functions depending on the temperature and parameters of the model is studied. A schematic phase diagram is plotted. It is shown that the thermodynamics of the system is mainly determined by elementary excitations with the entangled spin and orbital degrees of freedom.

Abstract:
We proceed from the premise that the spectrum of elementary excitations in the normal component in Landau's theory of superfluidity should depend on the superfluid helium temperature. This leads to generalization of the Landau superfluidity criterion. On this basis, taking into account available experimental data on inelastic neutron scattering, it is shown that, in addition to phonon--roton excitations, there is one more type of elementary excitations in superfluid helium, which we called helons. The energy spectrum with such a momentum dependence was first proposed by Landau. The helon energy spectrum shape and its temperature dependence make it possible to explain the singular behavior of the heat capacity of superfluid helium near its phase transition to the normal state.

Abstract:
We have found the elementary excitations of the exactly solvable BCS model for a fixed number of particles. These turn out to have a peculiar dispersion relation, some of them with no counterpart in the Bogoliubov picture, and unusual counting properties related to an old conjecture made by Gaudin. We give an algorithm to count the number of excitations for each excited state and a graphical interpretation in terms of paths and Young diagrams. For large systems the excitations are described by an effective Gaudin model, which accounts for the finite size corrections to BCS.