Related papers: Classical spin Hamiltonians are context-sensitive …
We introduce a new formalisation of languages, called keyboards. We consider a set of elementary operations (writing/erasing a letter, going to the right or to the left,...) and we define a keyboard as a set of finite sequences of such…
Near-integrability is usually associated with smooth small perturbations of smooth integrable systems. Studying integrable mechanical Hamiltonian flows with impacts that respect the symmetries of the integrable structure provides an…
The prospect of AGI instantiated on quantum substrates motivates the development of mathematical frameworks that enable direct comparison of their operation in classical and quantum environments. To this end, we introduce a Hamiltonian…
A physical self-learning machine can be defined as a nonlinear dynamical system that can be trained on data (similar to artificial neural networks), but where the update of the internal degrees of freedom that serve as learnable parameters…
In a vast class of systems, which includes members as diverse as sedimenting particles and bird flocks, interactions do not stem from a potential, and are in general nonreciprocal. Thus, it is not possible to define a conventional energy…
Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…
It is well known that the dynamics of a Hamiltonian system depends crucially on whether or not it possesses nonlinear resonances. In the generic case, the set of nonlinear resonances consists of independent clusters of resonantly…
Stoquastic Hamiltonians are characterized by the property that their off-diagonal matrix elements in the standard product basis are real and non-positive. Many interesting quantum models fall into this class including the Transverse field…
Efficiently characterising quantum systems, verifying operations of quantum devices and validating underpinning physical models, are central challenges for the development of quantum technologies and for our continued understanding of…
We derive explicit closed-form matrix representations of Hamiltonians drawn from tensored algebras, such as quantum spin Hamiltonians. These formulas enable us to soft-code generic Hamiltonian systems and to systematize the input data for…
We provide a reviewlike introduction into the quantum mechanical formalism related to non-Hermitian Hamiltonian systems with real eigenvalues. Starting with the time-independent framework we explain how to determine an appropriate domain of…
We propose a method for obtaining effective classical Hamiltonians \cal H for many-body quantum spin systems with large spins. This method uses the coherent-state representation of the partition function Z and the cumulant expansion in…
We consider here the problem of a "giant spin", with spin quantum number S>>1, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model describes the low-energy properties of magnetic…
We study cosmological perturbation theory with scalar field and pressureless dust in the Hamiltonian formulation, with the dust field chosen as a matter-time gauge. The corresponding canonical action describes the dynamics of the scalar…
A canonical Hamiltonian formalism is derived for a class of Ermakov systems specified by several different frequency functions. This class of systems comprises all known cases of Hamiltonian Ermakov systems and can always be reduced to…
Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures…
We consider quantum systems which interact strongly with a rapidly varying environment and derive a Schrodinger-like equation which describes the time evolution of the average wave function. We show that the corresponding Hamiltonian can be…
Infinite quasiperiodic arrangements in space, such as quasicrystals, are typically described as projections of higher-dimensional periodic lattices onto the physical dimension. The concept of a reference higher-dimensional space, called a…
Non-Hermitian Hamiltonians provide an alternative perspective on the dynamics of quantum and classical systems coupled non-conservatively to an environment. Once primarily an interest of mathematical physicists, the theory of non-Hermitian…
The non-Hermitian formalism is used at present in many papers for the description of open quantum systems. A special language developed in this field of physics which makes it difficult for many physicists to follow and to understand the…