Energy-momentum Dispersion Relation Research Articles

A novel translationally invariant supersymmetric chain with inverse-square interactions: partition function, thermodynamics and criticality

Abstract We introduce a novel family of translationally invariant su ( m | n ) supersymmetric spin chains with long-range interaction not directly associated with a root system. We study the symmetries of this model, establishing in particular the existence of a boson–fermion duality characteristic of this type of system. Taking advantage of the relation of the new chains with an associated many-body supersymmetric spin dynamical model, we are able to compute their partition function in closed form for all values of m and n and for an arbitrary number of spins. When both m and n are even, we show that the partition function factorizes as the product of the partition functions of two supersymmetric Haldane–Shastry spin chains, which in turn leads to a simple expression for the thermodynamic free energy per spin in terms of the Perron eigenvalue of a suitable transfer matrix. We use this expression to study the thermodynamics of a large class of these chains, showing in particular that the specific heat presents a single Schottky peak at approximately the same temperature as a suitable k-level model. We also analyze the critical behavior of the new chains, and in particular, the ground-state degeneracy and the existence of low-energy excitations with a linear energy–momentum dispersion relation. In this way, we show that the only possible critical chains are those with m = 0 , 1 , 2 . In addition, using the explicit formula for the partition function we are able to establish the criticality of the su ( 0 | n ) and su ( 2 | n ) chains with even n, and to evaluate the central charge of their associated conformal field theory.

Nonthermal acceleration radiation of atoms near a black hole in presence of dark energy

We investigate how dark energy affects atom-field interaction. To this end, we consider acceleration radiation of a freely falling atom close to a Schwarzschild black hole (BH) in the presence of dark energy characterized by a positive cosmological constant $\mathrm{\ensuremath{\Lambda}}$. The resulting spacetime is endowed with a BH and a cosmological (or de Sitter) horizon. Our consideration is a nonextremal ($1+1$)-dimensional geometry with horizons far apart, giving rise to a flat Minkowski-like region in between the two horizons. Assuming a scalar (spin-0) field in a Boulware-like vacuum state, and by using a basic quantum optics approach, we numerically achieve excitation probabilities for the atom to detect a photon as it falls toward the BH horizon. It turns out that the nature of the emitted radiation deeply drives its origin from the magnitude of $\mathrm{\ensuremath{\Lambda}}$. In particular, radiation emission is enhanced due to dilation of the BH horizon by dark energy. Also, we report an oscillatory nonthermal spectrum in the presence of $\mathrm{\ensuremath{\Lambda}}$, and these oscillations, in a varying degree, also depend on BH mass and atomic excitation frequency. We conjecture that such a hoedown may be a natural consequence of a constrained motion due to the bifurcate Killing horizon of the given spacetime. The situation is akin to the Parikh-Wilzcek tunneling approach to Hawking radiation where the presence of extra contributions to the Boltzmann factor deforms the thermality of flux. It apparently hints at field satisfying a modified energy-momentum dispersion relation within classical regime of general relativity arising as an effective low energy consequence of an underlying quantum gravity theory. Our findings may signal new ways of conceiving the subtleties surrounding the physics of dark energy.

Zone-Folded Quasi-bound State Metasurfaces with Customized, Symmetry-Protected Energy-Momentum Relations

Energy-momentum (dispersion) relations are a foundational framework for photonic device design, but our incomplete command thereof still limits key technologies. For instance, narrowband optical combiners for augmented reality should ideally reflect with unitary efficiency selected wavelengths that encode the artificial information over a large range of oblique incident angles, yet they are conventionally severely limited in field of view by dispersion. Here, we engineer nonlocal metasurfaces to support quasi-bound states in continuum with zero first-order resonant frequency dispersion at any desired quasi-momentum by exploiting a zone-folding technique that leverages a change in the lattice family. Our platform thereby advances photonic devices by enabling unprecedented control over the energy-momentum properties of nonlocal states, rationally controlled through a perturbation scheme that produces minimal distortion to non-resonant light.

Viscous dissipation in a gas of one-dimensional fermions with generic dispersion

A well-known feature of the classical monoatomic gas is that its bulk viscosity is strongly suppressed because the single-particle dispersion is quadratic. On the other hand, in condensed matter systems the effective single-particle dispersion is altered by lattice effects and interactions. In this work, we study the bulk viscosity of one-dimensional Fermi gases with generic energy-momentum dispersion relations. As an application, viscous dissipation arising from lattice effects is analyzed for the tight-binding model. In addition, we investigate how weak interactions affect the bulk viscosity. Finally, we discuss viscous dissipation in the regime in which the Fermi gas is not fully equilibrated, as can occur when the system is driven at frequencies that exceed the rate of fermion backscattering. In this case, the Fermi gas is described by three bulk viscosities, which we obtain for a generic single-particle dispersion.

The effects of the covariant generalized uncertainty principle on quantum mechanics

One can use the generalized uncertainty principle (GUP) to incorporate the minimum measurable length in quantum gravity. It may be interesting to have a minimal time interval as well as the minimal length in the relativistic version of quantum mechanics in the presence of the gravitational effects. In this paper, we considered a covariant version of the GUP to investigate the effects of both the minimal time and the minimal length. Using the covariant GUP, the energy–momentum dispersion relation was modified. Starting with the modified dispersion relation, the corrections to the wave function were obtained and the problems of the particle in a box and the hydrogen atom were revisited. Considering the minimal time may be an interesting new topic, which is not widely studied before. It may lead to new results that can open a new window into quantum gravity.

Unraveling Atomic and Electronic Surface Structure and Dynamics from Angular Photoelectron Distributions

Angle-resolved photoelectron spectroscopy (ARPES) is a powerful tool in solid state sciences. Beside the direct measurement of the energy-momentum dispersion relation, the angular distribution of the photoelectron current reveals the structural environment of the emitting atoms via photoelectron diffraction effects. Moreover, in the case of molecular layers, the angular distribution of emission from molecular orbitals can be directly related to their charge density distribution via so-called orbital tomography. In the present paper we summarize our efforts undertaken over the past 12 years to add the dimension of time to these two methods via pump-probe experiments with femtosecond resolution. We give a comprehensive introduction to standard ARPES and time-resolved two photon photoemission and then focus on our efforts towards time-resolved versions of photoelectron diffraction and orbital tomography. Both, optimization of experimental parameters and data acquisition procedures, as well as new numerical tools are needed in order to realize such challenging full stop missing after experiments.

Interpolating ’t Hooft model between instant and front forms

The 't Hooft model, i.e., the two-dimensional quantum chromodynamics in the limit of infinite number of colors, is interpolated by an angle parameter $\ensuremath{\delta}$ between $\ensuremath{\delta}=0$ for the instant form dynamics (IFD) and $\ensuremath{\delta}=\ensuremath{\pi}/4$ for the light-front dynamics (LFD). With this parameter $\ensuremath{\delta}$, we formulate the interpolating mass gap equation which takes into account the nontrivial vacuum effect on the bare fermion mass to find the dressed fermion mass. Our interpolating mass gap solutions not only reproduce the previous IFD result at $\ensuremath{\delta}=0$ as well as the previous LFD result at $\ensuremath{\delta}=\ensuremath{\pi}/4$ but also link them together between the IFD and LFD results with the $\ensuremath{\delta}$ parameter. We find the interpolation angle independent characteristic energy function which satisfies the energy-momentum dispersion relation of the dressed fermion, identifying the renormalized fermion mass function and the wave function renormalization factor. The renormalized fermion condensate is also found independent of $\ensuremath{\delta}$, indicating the persistence of the nontrivial vacuum structure even in the LFD. Using the dressed fermion propagator interpolating between IFD and LFD, we derive the corresponding quark-antiquark bound-state equation in the interpolating formulation verifying its agreement with the previous bound-state equations in the IFD and LFD at $\ensuremath{\delta}=0$ and $\ensuremath{\delta}=\ensuremath{\pi}/4$, respectively. The mass spectra of mesons bearing the feature of the Regge trajectories are found independent of the $\ensuremath{\delta}$-parameter reproducing the previous results in LFD and IFD for the equal mass quark and antiquark bound states. The Gell-Mann-Oakes-Renner relation for the pionic ground-state in the zero fermion mass limit is confirmed indicating that the spontaneous breaking of the chiral symmetry occurs in the 't Hooft model regardless of the quantization for $0\ensuremath{\le}\ensuremath{\delta}\ensuremath{\le}\ensuremath{\pi}/4$. We obtain the corresponding bound-state wave functions and discuss their reference frame dependence with respect to the frame independent LFD result. Applying them for the computation of the so-called quasi-parton distribution functions now in the interpolating formulation between IFD and LFD, we note a possibility of utilizing not only the reference frame dependence but also the interpolation angle dependence to get an alternative effective approach to the LFD-like results.

Quantum field theory of space-like neutrino

We performed a Lorentz covariant quantization of the spin-1/2 fermion field assuming the space-like energy-momentum dispersion relation. We achieved the task in the following steps: (i) determining the unitary realizations of the inhomogenous Lorentz group in the preferred frame scenario by means of the Wigner–Mackey induction procedure and constructing the Fock space; (ii) formulating the theory in a manifestly covariant way by constructing the field amplitudes according to the Weinberg method; (iii) obtaining the final constraints on the amplitudes by postulating a Dirac-like free field equation. Our theory allows to predict all chiral properties of the neutrinos, preserving the Standard Model dynamics. We discussed the form of the fundamental observables, energy and helicity, and show that non-observation of the +tfrac{1}{2} helicity state of the neutrino and the -tfrac{1}{2} helicity state of the antineutrino could be a direct consequence of the “tachyoneity” of neutrinos at the free level. We found that the free field theory of the space-like neutrino is not invariant under the C and P transformations separately but is CP-invariant. We calculated and analyzed the electron energy spectrum in tritium decay within the framework of our theory and found an excellent agreement with the recent measurement of KATRIN. In our formalism the questions of negative/imaginary energies and the causality problem does not appear.

5-Dimensional SO(1,4)-invariant action as an origin to the Magueijo-Smolin Doubly Special Relativity proposal

In this paper we discuss how the Magueijo-Smolin Doubly Special Relativity proposal may be obtained from a singular Lagrangian action. The deformed energy-momentum dispersion relation rises as a particular gauge, whose covariance imposes the non-linear Lorentz group action. Moreover, the additional invariant scale is present from the beginning as a coupling constant to a gauge auxiliary variable. The geometrical meaning of the gauge fixing procedure and its connection to the free relativistic particle are also described.

Engineering the Spectral and Spatial Dispersion of Thermal Emission via Polariton-Phonon Strong Coupling.

Strong coupling between optical modes can be implemented into nanophotonic design to modify the energy-momentum dispersion relation. This approach offers potential avenues for tuning the thermal emission frequency, line width, polarization, and spatial coherence. Here, we employ three-mode strong coupling between propagating and localized surface phonon polaritons, with zone-folded longitudinal optic phonons within periodic arrays of 4H-SiC nanopillars. Energy exchange, mode evolution, and coupling strength between the three polariton branches are explored experimentally and theoretically. The influence of strong coupling upon the angle-dependent thermal emission was directly measured, providing excellent agreement with theory. We demonstrate a 5-fold improvement in the spatial coherence and 3-fold enhancement of the quality factor of the polaritonic modes, with these hybrid modes also exhibiting a mixed character that could enable opportunities to realize electrically driven emission. Our results show that polariton-phonon strong coupling enables thermal emitters, which meet the requirements for a host of IR applications in a simple, lightweight, narrow-band, and yet bright emitter.

Strain-Induced Ultrahigh Electron Mobility and Thermoelectric Figure of Merit in Monolayer α-Te.

In line with the classic phonon-glass electron-crystal (PGEC) paradigm, semiconducting and semimetallic multinary compounds remain the cornerstone of the state-of-the-art thermoelectric materials. By contrast, elemental PGEC is very rare. In this work, we report a thermoelectric study of monolayer α-Te by first-principles calculations and solving the parameter-free Boltzmann transport equation. It is found that monolayer α-Te possesses high electron mobility (about 2500 cm2 V-1 s-1) at room temperature due to small effective mass, low phonon frequencies, and thus a restricted phase space for electron-phonon scattering. In monolayer α-Te, the electrons near the conduction band edge are mainly scattered by the heavily populated quadratically dispersing out-of-plane acoustic (ZA) phonon modes. The thermoelectric figure of merit (ZT) for n-type monolayer α-Te is 0.55 at 300 K and 1.46 at 700 K. Notably, tensile strain stiffens the ZA modes, yielding a linear energy-momentum dispersion relation and the removal of the diverging thermal population of ZA phonons. Consequently, the electron mobility is enhanced. At a 4% tensile strain, the electron mobility can reach up to 8000 cm2 V-1 s-1 at room temperature while the thermal conductivity is almost unaffected, yielding a state-of-the-art ZT value of 0.94 and 2.03 in n-type monolayer α-Te at 300 and 700 K, respectively. For completeness, the thermoelectric study of p-type monolayer α-Te is also conducted. These results beckon further experiments toward high-performance α-Te-based thermoelectric materials via doping, alloying, and compositing.

Perfectly matched layers for Schrödinger-type equations with nontrivial energy–momentum dispersion

The construction of perfectly-matched-layer (PML) boundary conditions is extended to wave equations with non-trivial energy–momentum dispersion relation. Complex coordinate extension is based upon the relative sign between the surface-normal component of group velocity and the k-vector. This ensures selective damping of propagating and counter-propagating modes at the simulation boundaries. Moreover, the technical complexity of the PML method can be inferred from the energy–momentum dispersion relation of the underlying wave equation, respectively, the finite-difference scheme employed. The PML transform is derived for selected Schrödinger-type (i.e. first-order-in-time) kinetic transport equations. Spectral analysis demonstrates proper damping behaviour of out-propagating modes. Results are presented for the Schrödinger equation for particles and holes, the s- and p-wave Bogoliubov–de Gennes equation, the Dirac equation, and the Dohnal k⋅p model. Where available, a comparison to previous PML formulations is made.

Quantum walk versus classical wave: Distinguishing ground states of quantum magnets by spacetime dynamics

We investigate the wavepacket spreading after a single spin flip in prototypical two-dimensional ferromagnetic and antiferromagnetic quantum spin systems. We find characteristic spatial magnon density profiles: While the ferromagnet shows a square-shaped pattern reflecting the underlying lattice structure, as exhibited by quantum walkers, the antiferromagnet shows a circular-shaped pattern which hides the lattice structure and instead resembles a classical wave pattern. We trace these fundamentally different behaviors back to the distinctly different magnon energy-momentum dispersion relations and also provide a real-space interpretation. Our findings point to new opportunities for real-time, real-space imaging of quantum magnets both in materials science and in quantum simulators.

An electrically induced probe of the modes of a plasmonic multilayer stack.

A new single-image acquisition technique for the determination of the dispersion relation of the propagating modes of a plasmonic multilayer stack is introduced. This technique is based on an electrically-driven, spectrally broad excitation source which is nanoscale in size: the inelastic electron tunnel current between the tip of a scanning tunneling microscope (STM) and the sample. The resulting light from the excited modes of the system is collected in transmission using a microscope objective. The energy-momentum dispersion relation of the excited optical modes is then determined from the angle-resolved optical spectrum of the collected light. Experimental and theoretical results are obtained for metal-insulator-metal (MIM) stacks consisting of a silicon oxide layer (70, 190 or 310 nm thick) between two gold films (each with a thickness of 30 nm). The broadband characterization of hybrid plasmonic-photonic transverse magnetic (TM) modes involved in an avoided crossing is demonstrated and the advantages of this new technique over optical reflectivity measurements are evaluated.

Nonlocal fermions and the entropy volume law

To produce a fermionic model exhibiting an entanglement entropy volume law, we propose a particular version of nonlocality in which the energy-momentum dispersion relation is effectively randomized at the shortest length scales while preserving translation invariance. In contrast to the ground state of local fermions, exhibiting an entanglement entropy area law with logarithmic corrections, the entropy of nonlocal fermions is extensive, scaling as the volume of the subregion and crossing over to the anomalous fermion area law at scales larger than the locality scale, {\alpha}. In the 1-d case, we are able to show that the central charge appearing in the universal entropy expressions for large subregions is simply related to the locality scale. These results are demonstrated by exact diagonalizations of the corresponding discrete lattice fermion models. Within the Ryu-Takayanagi holographic picture, the relation between the central charge and the locality scale suggest a dual spacetime in which the size of the flat UV portion and the radius of AdS in the IR are both proportional to the locality scale, {\alpha}.

Nonsaturating large magnetoresistance in the high carrier density nonsymmorphic metal CrP

The band structure of high carrier density metal CrP features an interesting crossing at the Y point of the Brillouin zone. The crossing, which is protected by the nonsymmorphic symmetry of the space group, results in a hybrid, semi-Dirac-like energy-momentum dispersion relation near Y. The linear energy-momentum dispersion relation along Y-$\Gamma$ is reminiscent of the observed band structure in several semimetallic extremely large magnetoresistance (XMR) materials. We have measured the transverse magnetoresistance of CrP up to 14 T at temperatures as low as $\sim$ 16 mK. Our data reveal a nonsaturating, quadratic magnetoresistance as well as the behaviour of the so-called `turn-on' temperature in the temperature dependence of resistivity. Despite the difference in the magnitude of the magnetoresistance and the fact that CrP is not a semimetal, these features are qualitatively similar to the observations reported for XMR materials. Thus, the high-field electrical transport studies of CrP offer the prospect of identifying the possible origin of the nonsaturating, quadratic magnetoresistance observed in a wide range of metals.

Giant magnonlike solution in Sch5×S5

In this paper we have found a classical giant magnon-like solution with both infinite and finite angular momentum moving in Sch_5 x S^5 with B-field, which is believed to be dual to dipole-deformed N=4 super Yang-Mills theory. This string state propagates as a point particle in non-trivial subspace of the Sch_5 space but shows a giant magnon-like property in the S^2 subspace. We derive the energy-momentum dispersion relations and their finite-size correction for the case of finite but large angular momentum.

The effect of modified dispersion relation on dumb holes

In this paper, we will deform the usual energy–momentum dispersion relation of a photon gas at an intermediate scale between the Planck and electroweak scales. We will demonstrate that such a deformation can have nontrivial effects on the physics of dumb holes. So, motivated by the physics of dumb holes, we will first analyze the effect of such a deformation on thermodynamics. Then, we observe that the velocity of sound also gets modified due to such a modification of the thermodynamics. This changes the position of the horizon of dumb holes, and the analogous Hawking radiation from a dumb hole. Therefore, dumb holes can be used to measure the deformation of the usual energy–momentum dispersion relation.

The variation of photon speed with photon frequency in quantum gravity

In the present work, an expression for Planck mass or Planck energy is derived by equating the Compton wavelength with the gravitational radius of the Kerr rotating body. Using the modified photon energy–momentum dispersion relation, the variation of the photon propagation speed with photon frequency is derived. It is found that, the photon propagation speed, depends on the frequency of the photon, the rotation parameter of the Kerr rotating body and also on the polarization state of the photon. Quantum gravity effect could be seen from the derived results for the photon propagation speed.

Spotlighting phase separation in Rashba spin-orbit coupled Bose–Einstein condensates in two dimensions

We study the system of spin-orbit (SO) coupled Bose–Einstein condensates (BEC) with Rabi coupling in quasi-two dimensions characterized by unequal Rashba and Dresselhaus couplings. The ground state properties and the phase diagram of the system are studied within the mean-field approximation at T = 0. The energy-momentum dispersion relation corresponding to the single-particle ground state exhibits an infinitely degenerate Rashba ring, whose degeneracy is destroyed by the Rabi coupling, leading to a single-point lowest energy. The effect of Rabi coupling and interaction in the system show up three different phases, namely stripe, plane wave and zero momentum phase. At a particular parametric condition, the system admits a critical point separating all three different phases, known as the tri-critical point. For further insight, the momentum distribution, the energy and the longitudinal/transverse spin polarization corresponding to the quantum phases are comprehensively discussed.