Kinetic theory of desorption: Energy and angular distributions

The transformation of interacting fermions into free bosons known e.g. from the solution of the Luttinger model is reconsidered in a condensed version which combines all fermionic degrees of freedom in a single boson field. This simplifies calculations as compared to the usual separate treatment of the charge degrees of freedom. The representation of the fermions is exact. The Thirring-Schwinger model is described and solved with special emphasis on boundary effects. Implications for massive fermions are briefly mentioned.     

Large N expansion for strongly-coupled boson–fermion mixtures

We study a many-body mixture of an equal number of bosons and two-component fermions with a strong contact attraction. In this system bosons and fermions can be paired into composite fermions. We construct a large N extension where both bosons and fermions have the extra large N degrees of freedom and the boson–fermion interaction is extended to a four-point contact interaction which is invariant under the O(N) group transformation, so that the composite fermions become singlet in terms of the O(N) group. It is shown that such O(N) singlet fields have controllable quantum fluctuations suppressed by 1/N factors and yield a systematic 1/N-expansion in terms of composite fermions. We derive an effective action described by composite fermions up to the next-to-leading-order terms in the large N expansion, and show that there can be the BCS superfluidity of composite fermions at sufficiently low temperatures.     

Vaidya-Bonner黑洞的费米子隧穿

运用费米子隧穿的理论,对Vaidya-Bonner黑洞的费米子Hawking辐射进行研究.使用随动坐标变换,并假设γ^μ矩阵的一个合理形式,从而得到了Vaidya-Bonner黑洞的自旋为1/2的粒子的隧穿辐射行为. 关键词： Vaidya-Bonner黑洞 Dirac方程 Hawking辐射 费米子隧穿     

Corner transfer matrices for the Ising model

We consider corner transfer matrices for the regular Ising model and show that finding a diagonal representation is a soluble problem in interacting fermions. We show how the requirement of having an invertible diagonalising transformation determines which representation must be used and explain why Baxter's original solution of the problem did not produce such an invertible transformation.     

Realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions

Quantum computers are in hot-spot with the potential to handle more complex problems than classical computers can.Realizing the quantum computation requires the universal quantum gate set {T,H,CNOT} so as to perform any unitary transformation with arbitrary accuracy.Here we first briefly review the Majorana fermions and then propose the realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions.Elementary cells consist of a quantum anomalous Hall insulator surrounded by a topological superconductor with electric gates and quantum-dot structures,which enable the braiding operation and the partial exchange operation.After defining a qubit by four chiral Majorana fermions,the singlequbit T and H quantum gates are realized via one partial exchange operation and three braiding operations,respectively.The entangled CNOT quantum gate is performed by braiding six chiral Majorana fermions.Besides,we design a powerful device with which arbitrary two-qubit quantum gates can be realized and take the quantum Fourier transform as an example to show that several quantum operations can be performed with this space-limited device.Thus,our proposal could inspire further utilization of mobile chiral Majorana edge states for faster quantum computation.     

New overlap construction of Weyl fermions on the lattice

In a recent article Hasenfratz and von Allmen have suggested a fixed point action for two flavors of Weyl fermions on the lattice with gauge group SU(2). The block-spin transformation they use maps the chiral and vector symmetries of the underlying vector theory onto two equations of the Ginsparg–Wilson (GW) type. We show that an overlap Dirac operator can be constructed which solves both GW equations simultaneously. We discuss the properties of this overlap operator and its projection onto lattice Weyl fermions which seems to be free of artefacts, in particular the projection operators are independent of the gauge field.     

Parity,baryon number and supersymmetry

Space reflection induces a transformation in the pseudo-Lie algebra of generators of symmetries and supersymmetries. If there is a supermultiplet in the thepry in which the baryon number is zero for bosons and ± 1 for fermions then the structure of the pseudo-Lie algebra is simple and therefore the space reflection transformation can be studied in detail. It turns out that the space reflection transformation fixes uniquely the structure of the pseudo-Lie algebra as far as the generators of supersymmetries are concerned.     

Nonperturbative canonical formulation and Ward-Takahashi relations for quantum many-body systems at finite temperatures

A nonperturbative canonical field-theoretic approach to Matsubara's finite temperature quantum many-body theory is presented. The finite temperature Ward-Takahashi relations for the phase transformation, the Galilean transformation and general time-independent continuous transformations are derived for both fermions and bosons with interactions. The finite temperature Ward-Takahashi relations for nonconserved currents and the finite temperature Goldstone's theorem are also discussed.     

Fixed point action for the massless lattice Schwinger model

We determine non-perturbatively the fixed-point action for fermions in the two-dimensional U(1) gauge (Schwinger) model. This is done by iterating a block spin transformation in the background of non-compact gauge field configurations sampled according to the (perfect) Gausian measure. The resulting action has 123 independent couplings, is bilinear in the Grassmann fields, gauge invariant by the compact gauge transporters considered, and localized within a 7 × 7 lattice centered around one of the fermions. We then simulate the model at various values of β and compare with results obtained with the Wilson fermion action. We find excellent improvement for the observables studied (propagators and masses).     

Variational estimates of chiral order parameter in 1+1 dimensional lattice QCD

We discuss analytically the vacuum structure and chiral-symmetry breaking in 1+1 dimensional lattice QCD with naive and Wilson fermions, using a unitary transformation and the variational method developed recently. As an example, the chiral order parameter is evaluated systematically for any coupling constant and fermion mass by including the multilink-terms in the transformation. The expected scaling behavior is observed. Our results are consistent with the continuum predictions.     

Hawking Radiation via Damour-Ruffini Method in Squashed Charged Rotating Kaluza-Klein Black Holes

Using the Damour-Ruffini method, Hawking radiation of charged particles from squashed charged rotating five-dimensional Kaluza-Klein black holes is investigated extensively. Under the generalized tortoise coordinate transformation, Hawking temperature of the black holes is calculated by using charged scalar particles and Dirac fermions respectively. We find that the obtained Hawking temperature for charged Dirac fermions is the same as for charged scalar particles. What’s more, the spectrum of Hawking radiation contains the information of the size of the extra dimension, which could provide insight for further investigation of large extra dimensions in the future.     

Even dimensional generalization of Chern-Simons action and new gauge symmetry

We propose a new even-dimensional action which shares close algebraic similarities with the Chern-Simons action and thus possesses a topological nature. This action has a new type of gauge symmetry in the sense that adjoint representation is not enough to close the gauge transformation and gauge fermions are incorporated. Quaternionic structure emerges as a natural algebra to control the different natures of even forms, odd forms, bosons and fermions. We claim that the bundle structure in consideration is mathematically a new object.     

Studies on the Chiral Order Parameter in the Schwinger Model

Based on an analytical technique using a unitary transformation and the variational method, we study the chiral order parameter in the Schwinger model in the lattice formalism with Kogut-Susskind fermions. The fermion condensate (ψψ)fo r any coupling constant and fermion mass are calculated. Chiral symmetry is shown to be broken in the massless limit and good scaling behavior is obtained.     

Exact transformation for spin-charge separation of spin-1/2 fermions without constraints

We demonstrate an exact local transformation which maps a purely Fermionic many-body system to a system of spinful bosons and spinless fermions, demonstrating a possible path to a non-Fermi-liquid state. We apply this to the half-filled Hubbard model and show how the transformation maps the ordinary spin half Fermionic degrees of freedom exactly and without introducing Hilbert space constraints to a chargelike quasicharge fermion and a spinlike quasispin Boson while preserving all the symmetries of the model. We present approximate solutions with localized charge which emerge naturally from the Hubbard model in this form. Our results strongly suggest that charge tends to remain localized for large values of the Hubbard U.     

Anomalies in PT-Symmetric Quantum Field Theory

It is shown that a version of PT-symmetric electrodynamics based on an axial-vector current coupling massless fermions to the photon possesses anomalies and so is rendered nonrenormalizable. An alternative theory is proposed based on the conventional vector current constructed from massive Dirac fields, but in which the PT transformation properties of electromagnetic fields are reversed. Such a theory seems to possess many attractive features.     

Functional bosonization of interacting fermions in arbitrary dimensions

We bosonize the long-wavelength excitations of interacting fermions in arbitrary dimension by directly applying a suitable Hubbard-Stratonowich transformation to the Grassmannian generating functional of the fermionic correlation functions. With this technique we derive a surprisingly simple expression for the singleparticle Greens-function, which is valid for arbitrary interaction strength and can describe Fermi- as well as Luttinger liquids. Our approach sheds further light on the relation between bosonization and the random-phase approximation, and enables us to study screening in a nonperturbative way.     

Gravitational anomalies and Schwinger terms

A BRST transformation incorporating general coordinate, Lorentz and Weyl transformations is defined. The variation of the effective action for fermions moving in an external gravitational field is calculated using an extended BRST analysis. InD=2 dimensions the Schwinger terms appearing in the equal time commutators of energy momentum tensors are related to the gravitational and Weyl anomalies for a massless spin 0 and a massless spin 1/2 model, respectively.     

A strongly attractive Fermi gas in an optical lattice

We study strongly attractive fermions in an optical lattice superimposed by a trapping potential. We calculate the densities of fermions and condensed bound molecules at zero temperature. There is a competition between dissociated fermions and molecules leading to a reduction of the density of fermions at the trap center.     

Plasma oscillations in a one-dimensional many-fermion system

Following the Shevchik technique, a model Hamiltonian of collective oscillations (plasmons) in a one-dimensional system of complete degenerate fermions is obtained in terms of the Tomonaga boson operators. This Hamiltonian is diagonalized by means of the Mattis and Lieb canonical transformation and the plasma frequency is derived. The equation-of-motion method is applied in the RPA in order to include the coupling between the collective and individual degrees of freedom. The generalization to finite temperatures is performed and connection with the Tomonaga model is discussed.     

Quantum spins on star graphs and the Kondo model

We study the XX model for quantum spins on the star graph with three legs (i.e., on a Y  -junction). By performing a Jordan–Wigner transformation supplemented by the introduction of an auxiliary space we find a Kondo Hamiltonian of fermions, in the spin 1 representation of su(2)$\mathit{su}(2)$, locally coupled with a magnetic impurity. In the continuum limit our model is shown to be equivalent to the 4-channel Kondo model coupling spin-1/2 fermions with a spin-1/2 impurity and exhibiting a non-Fermi liquid behavior. We also show that it is possible to find an XY model such that – after the Jordan–Wigner transformation – one obtains a quadratic fermionic Hamiltonian directly diagonalizable.