相关论文: Fermionic observables in Numerical Stochastic Pert…
Determining the steady state of an open quantum system is crucial for characterizing quantum devices and studying various physical phenomena. Often, computing a single steady state is insufficient, and it is necessary to explore its…
A review is given of the presymplectic approach to relativistic physical systems and of the determination of their Dirac's observables. After relativistic mechanics and Nambu string, the Dirac's observables of Yang-Mills theory with…
Recently, properties of the fixed point action for fermion theories have been pointed out indicating realization of chiral symmetry on the lattice. We check these properties by numerical analysis of the spectrum of a parametrized fixed…
We propose a multipole representation of the Fermi-Dirac function and the Fermi operator, and use this representation to develop algorithms for electronic structure analysis of metallic systems. The new algorithm is quite simple and…
We study Sturm-Liouville operators on closed sets of a special structure, which are sometimes referred as time scales and often appear in modelling various real processes. Depending on the set structure, such operators unify both…
We compute the lattice spacing corrections to the spectral density of the Hermitean Wilson Dirac operator using Wilson Chiral Perturbation Theory at NLO. We consider a regime where the quark mass $m$ and the lattice spacing $a$ obey the…
Many applications in Lattice field theory require to determine the Taylor series of observables with respect to action parameters. A primary example is the determination of electromagnetic corrections to hadronic processes. We show two…
We describe a method of construction of gauge-invariant operators (Dirac observables or ``evolving constants of motion'') from the knowledge of the eigenstates of the gauge generator in time-reparametrization invariant mechanical systems.…
In this thesis, we analyze unitary conformal field theories in three dimensional spaces by applying analytic conformal bootstrap techniques to correlation functions of non-scalar operators, in particular Majorana fermions. Via the analysis…
Infinite-dimensional control systems with outputs are considered in the Hamiltonian formulation with generalized coordinates. An explicit scheme for constructing a dynamic observer for this class of systems is proposed with arbitrary gain…
In this talk I propose a new computational scheme with overlap fermions and a fast algorithm to invert the corresponding Dirac operator.
We develop relativistic wave equations in the framework of the new non-hermitian ${\cal PT}$ quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of ${\cal…
The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by non-Hermitian Hamiltonians with parity-time $(\mathcal{PT})$ symmetry that are best understood as systems with…
The main issues of the spectral theory of Dirac operators are presented, namely: transformation operators, asymptotics of eigenvalues and eigenfunctions, description of symmetric and self-adjoint operators in Hilbert space, expansion in…
This paper deals with an inverse nodal problem for the Dirac differential operator with the discontinuity conditions inside the interval. We obtain a new approach for asymptotic expressions of the solutions and prove that the coefficients…
We report on an ongoing project to parametrize the Fixed-Point Dirac operator for massless quarks, using a very general construction which has arbitrarily many fermion offsets and gauge paths, the complete Clifford algebra and satisfies all…
The need to enforce fermionic antisymmetry in the nuclear many-body problem commonly requires use of single-particle coordinates, defined relative to some fixed origin. To obtain physical operators which nonetheless act on the nuclear…
By using a perturbation technique in critical point theory, we prove the existence of solutions for two types of nonlinear equations involving fractional differential operators.