Supersymmetry and electron-hole excitations in semiconductors at finite temperature

The fermionic and bosonic electron-hole low-lying excitations in a semiconductor are analyzed at finite temperature in a unified way following Nambu's quasi-supersymmetric approach for the BCS model of superconductivity. The effective lagrangian for the fermionic modes and for the bosonic low-lying collective excitations in the semiconductor is no longer supersymmetric in a conventional finite-temperature treatment. However, the bosonic excitations do not couple directly to the heat bath and as a result, quasi-supersymmetry is restored to the effective lagrangian when a redefinition of the coupling constant associated with the collective excitations is performed. Our result shows that although the mass and coupling parameters are now temperature dependent, the fermion and boson excited states pair together and can still be transmuted into one another.     

Cliffordization, spin, and fermionic star products

Deformation quantization is a powerful tool for quantizing theories with bosonic and fermionic degrees of freedom. The star products involved generate the mathematical structures which have recently been used in attempts to analyze the algebraic properties of quantum field theory. In the context of quantum mechanics they provide a quantization procedure for systems with either bosonic or fermionic degrees of freedom. We illustrate this procedure for a number of physical examples, including bosonic, fermionic, and supersymmetric oscillators. We show how non-relativistic and relativistic particles with spin can be naturally described in this framework.     

The boson-fermion hybrid representation formulation,I

A boson-fermion hybrid representation is presented. In this framework, a fermion system is described concurrently by the bosonic and the fermionic degrees of freedom. A fermion pair in this representation can be treated as a boson without violating the Pauli principle. Furthermore the “bosonic interactions” are shown to originate from the exchange processes of the fermions and can be calculated from the original fermion interactions. Both the formulation of the BFH representations for the even and odd nuclear systems are given. We find that the basic equation of the nuclear field theory (NFT) is just the usual Schrödinger equation in such a representation with the empirical NFT diagrammatic rules emerging naturally. This theory was numerically checked in the case of four nucleons moving in a single-j shell and the exactness of the theory was established.     

A hamiltonian with broken supersymmetry for the xenon isotopes

A hamiltonian with broken $\text{u}\text{(}\text{6}\text{2}\text{j+1)}$ supersymmetry is proposed that can describe collective excitations in nuclei with high-spin, single-j orbitals. Its bosonic part is identical with IBA, while the fermionic degrees of freedom, are characterized by the seniority quantum number. The ground state as well as excited energies of eight xenon isotopes with both odd and even mass are fairly well described by the so(6) limit of this hamiltonian with only one set of parameters.     

Scalar lattice gauge theory

Scalar lattice gauge theories are models for scalar fields with local gauge symmetries. No fundamental gauge fields, or link variables in a lattice regularization, are introduced. The latter rather emerge as collective excitations composed from scalars. For suitable parameters scalar lattice gauge theories lead to confinement, with all continuum observables identical to usual lattice gauge theories. These models or their fermionic counterpart may be helpful for a realization of gauge theories by ultracold atoms. We conclude that the gauge bosons of the standard model of particle physics can arise as collective fields within models formulated for other “fundamental” degrees of freedom.     

Master equation approach to conductivity of bosonic and fermionic carriers in one‐ and two‐dimensional lattices

The master equation approach to diffusive current of bosonic or fermionic carriers in one‐ and two‐dimensional lattices is discussed. This approach is shown to reproduce all known results of the linear response theory, including the integer quantum Hall effect for fermionic carriers. The main advantage of the approach is that it allows to calculate the current beyond the linear response regime where new effects are found. In particular, the Hall current can be inverted by changing orientation of the static force (electric field) relative to the primary axes of the lattice.     

Smooth non-Abelian bosonization

We present an extension of “smooth bosonization” to the non-Abelian case. We construct an enlarged theory containing both bosonic and fermionic fields which exhibits a local chiral gauge symmetry. A gauge fixing function depending on one real parameter allows us to interpolate smoothly between a purely fermionic and a purely bosonic representation. The procedure is, in the special case of bosonization, complementary to the approach based on duality.     

Rigid superstrings

A recently proposed bosonic string action containing a term proportional to the world sheet is supersymmetrized in the light-cone gauge. We compute the one-loop contribution to the β function of the new coupling constant and find that the asymptotic freedom present in the bosonic case is not destroyed by the addition of the fermionic degrees of freedom.     

Path integrals and linear canonical transformations

For a system withN bosonic or fermionic degrees of freedom I calculate the coherent state propagator, i.e. the matrix element between coherent states of the evolution operator, for a general quadratic Hamiltonian plus a source term, using the holomorphic form of the path integral. The analysis and the result obtained are used to discuss the transformation properties of the path integral for linear canonical transformations (Bogoliubov-Valatin trfs), a preliminary to the formulation of a geometric theory of path integral quantization.

     

A conjecture on the use of quantum algebras in the treatment of discrete systems

The interactions between atomic spin-states, and between them and an external radiation field, can be described in terms of quantum algebras by a trade-off of bosonic and fermionic degrees of freedom and q-deformed schemes. In this Letter we discuss the use of this concept concerning the calculation of a spin observable, like the spin squeezing.     

Supersymmetry in the problem of a fermion in an external nonabelian gauge field

The quantum-mechanical problem was considered of the motion of a Dirac particle in a nonabelian chromomagnetic field of the local isospin group SU(2). It was shown that the problem possesses supersymmetry. Supercharges were constructed, satisfying the standard superalgebra. The fermionic number operator coincides with the invariant spin operator of the Dirac equation. We clarified the features, in the given case, of supersymmetry, appearing in the anomaly of the commutation relations for the bosonic operators that was caused by the mutual tie of the bosonic (spatial and isospin) and the fermionic (spin) degrees of freedom for motion in the gauge field considered. It was demonstrated that the degeneracy of the vacuum (ground state) is removed by means of the spontaneous symmetry-breaking SU(2)U(1). The choice of a solution in the group U(1) is determined by the sign of the charge (color) of the particle in the ground state.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 40–44, February, 1989.     

Excitation Dynamics in Chain-Mapped Environments

The chain mapping of structured environments is a most powerful tool for the simulation of open quantum system dynamics. Once the environmental bosonic or fermionic degrees of freedom are unitarily rearranged into a one dimensional structure, the full power of Density Matrix Renormalization Group (DMRG) can be exploited. Beside resulting in efficient and numerically exact simulations of open quantum systems dynamics, chain mapping provides an unique perspective on the environment: the interaction between the system and the environment creates perturbations that travel along the one dimensional environment at a finite speed, thus providing a natural notion of light-, or causal-, cone. In this work we investigate the transport of excitations in a chain-mapped bosonic environment. In particular, we explore the relation between the environmental spectral density shape, parameters and temperature, and the dynamics of excitations along the corresponding linear chains of quantum harmonic oscillators. Our analysis unveils fundamental features of the environment evolution, such as localization, percolation and the onset of stationary currents.     

Are CP Violating Effects in the Standard Model Really Tiny?

We derive an effective action of the bosonic sector of the Standard Model by integrating out the fermionic degrees of freedom in the worldline approach. The CP violation due to the complex phase in the CKM matrix gives rise to CP-violating operators in the effective action. We calculate the prefactor of the appropriate next-to-leading order operators and give general estimates of CP violation in the bosonic sector of the Standard Model. In particular, we show that the effective CP violation for weak gauge fields is not suppressed by the Yukawa couplings of the light quarks and is much larger than the bound given by the Jarlskog determinant.     

Luttinger liquid of photons and spin-charge separation in hollow-core fibers

In this work we show that light-matter excitations (polaritons) generated inside a hollow-core one-dimensional fiber filled with two types of atoms, can exhibit Luttinger liquid behavior. We first explain how to prepare and drive this quantum-optical system to a strongly interacting regime, described by a bosonic two-component Lieb-Liniger model. Utilizing the connection between strongly interacting bosonic and fermionic systems, we then show how spin-charge separation could be observed by probing the correlations in the polaritons. This is performed by first mapping the polaritons to propagating photon pulses and then measuring the effective photonic spin and charge densities and velocities by analyzing the correlations in the emitted photon spectrum. The necessary regime of interactions is achievable with current quantum-optical technology.     

Supersymmetric Content of the Dirac and Duffin-Kemmer-Petiau Equations

We study subsolutions of the Dirac and Duffin-Kemmer-Petiau equations described in our earlier papers. It is shown that subsolutions of the Duffin-Kemmer-Petiau equations and those of the Dirac equation obey the same Dirac equation with some built-in projection operator. This covariant equation can be referred to as supersymmetric since it has bosonic as well as fermionic degrees of freedom.     

Supersymmetric gauge theories in quantum mechanics

A general construction for supersymmetric U(1) gauge invariant Hamiltonians in quantum mechanics is given. For a given number of fermionic and bosonic degrees of freedom it is shown that for four supercharges the interactions are determined uniquely, and coincide with the dimensionally reduced N = 1, d = 3 + 1 supersymmetric electrodynamics. With two supercharges one gets models which cannot be obtained through dimensional reduction. For two special choices of a parameter one recovers the dimensionally reduced d = 1 + 1 Weyl supersymmetric and Majorana supersymmetric electrodynamics.     

Supersymmetry transformations of instantons

Instantons in the simplest supersymmetric Yang-Mills theory are considered. We introduce bosonic and fermionic collective coordinates and study how they change under the supersymmetry transformations. The instanton measure is shown to be explicitly invariant under the transformations. We discuss the relation between quantum anomalies and the functional form of the instanton measure.