Related papers: Boundary conditions for quantum lattice systems
Based on a result by Yarotsky (J. Stat. Phys. 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site terms change the ground state of such a system…
This dissertation presents and prove the viability of a non-standard method for controlling the state of a quantum system by modifying its boundary conditions instead of relying on the action of external fields. The standard approach to…
The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems. We also show that a quantum…
The entanglement entropy of the ground state of a quantum lattice model with local interactions usually satisfies an area law. However, in 1D systems some violations may appear in inhomogeneous systems or in random systems. In our…
The dynamics of quantum field theories on bounded domains requires the introduction of boundary conditions on the quantum fields. We address the problem from a very general perspective by using charge conservation as a fundamental principle…
We present a general procedure for constructing lattices of qubits with a Hamiltonian composed of nearest-neighbour two-body interactions such that the ground state encodes a cluster state. We give specific details for lattices in one-,…
In a Hermitian system, bound states must have quantized energies, whereas extended states can form a continuum. We demonstrate how this principle fails for non-Hermitian systems, by analyzing non-Hermitian continuous Hamiltonians with an…
We analyze the global theory of boundary conditions for a constrained quantum system with classical configuration space a compact Riemannian manifold $M$ with regular boundary $\Gamma=\partial M$. The space $\CM$ of self-adjoint extensions…
The relationship between classical and quantum mechanics is usually understood via the limit $\hbar \rightarrow 0$. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity…
In this paper, we develop the framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show that they occur naturally in the…
In a configuration space whose boundary can be identified with a subset of its interior, a boundary condition can relate the behaviour of a function on the boundary and in the interior. Additionally, boundary values can appear as additive…
The so-called classical limit of quantum mechanics is generally studied in terms of the decoherence of the state operator that characterizes a system. This is not the only possible approach to decoherence. In previous works we have…
We investigate bosonic Gaussian quantum states on an infinite cubic lattice in arbitrary spatial dimensions. We derive general properties of such states as ground states of quadratic Hamiltonians for both critical and non-critical cases.…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
We assess two different non-equilibrium quantum Landauer bounds: the traditional approach based on the change in entropy, referred to as the `entropic bound', and one based on the details of the dynamical map, referred to as the…
We develop the idea that a natural link between Boltzmann schemes and finite volumes exists naturally: the conserved mass and momentum during the collision phase of the Boltzmann scheme induces general expressions for mass and momentum…
We construct a mathematically well--defined framework for the kinematics of Hamiltonian QCD on an infinite lattice in $\R^3$, and it is done in a C*-algebraic context. This is based on the finite lattice model for Hamiltonian QCD developed…
By imposing twisted boundary conditions on quark fields it is possible to access components of momenta other than integer multiples of 2pi/L on a lattice with spatial volume L^3. We use Chiral Perturbation Theory to study finite-volume…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
We describe here a novel way of defining Hamiltonians for quantum field theories (QFTs), based on the particle-position representation of the state vector and involving a condition on the state vector that we call an "interior-boundary…