Related papers: The quantum auxiliary linear problem & Darboux-Bac…
Bounds to the speed of evolution of a quantum system are of fundamental interest in quantum metrology, quantum chemical dynamics and quantum computation. We derive a time-energy uncertainty relation for open quantum systems undergoing a…
The use of a relational time in quantum mechanics is a framework in which one promotes to quantum operators all variables in a system, and later chooses one of the variables to operate like a ``clock''. Conditional probabilities are…
In this note, we analyze an abstract evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. We assume that the operator corresponding to the nondelayed part of the model generates an exponentially…
In our previous work \cite{LNS}, we constructed quasi-Casoratian solutions to the noncommutative $q$-difference two-dimensional Toda lattice ($q$-2DTL) equation by Darboux transformation, which we can prove produces the existing Casoratian…
A version of the iterated B\"acklund-Darboux transformation, where Darboux matrix takes a form of the transfer matrix function from the system theory, is constructed for the discrete canonical system and Non-Abelian Toda lattice. Results on…
While the quantum regression theorem (QRT) is the standard tool for computing multi-time correlation functions in open quantum systems, it relies on system-bath separability and an environment that remains in equilibrium, assumptions that…
New exact and asymptotic results for a quantum inverted oscillator, driven by the variable external force, are presented. To illustrate the advantages of our approach, we applied the obtained propagator to the descriptions of evolution the…
A brief non-technical review of the recent study of classical integrable structures in quantum integrable systems is given. It is explained how to identify the standard objects of quantum integrable systems (transfer matrices, Baxter's…
We solve the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups ${\cal U}% _{q}(X_{n})$ for $X_{n}=A_{1},$ $B_{n},$ $C_{n}$ and $D_{n}$. The tool is a modified version…
A formulation of quantum-classical hybrid dynamics is presented, which concerns the direct coupling of classical and quantum mechanical degrees of freedom. It is of interest for applications in quantum mechanical approximation schemes and…
Time-dependent linear differential equations are a common type of problem that needs to be solved in classical physics. Here we provide a quantum algorithm for solving time-dependent linear differential equations with logarithmic dependence…
Both the classical time-ordering and the Magnus expansion are well-known in the context of linear initial value problems. Motivated by the noncommutativity between time-ordering and time derivation, and related problems raised recently in…
The infinite time-evolving block decimation (iTEBD) algorithm [Phys. Rev. Lett. 98, 070201 (2007)] allows to simulate unitary evolution and to compute the ground state of one-dimensional quantum lattice systems in the thermodynamic limit.…
Quantum dynamical time-evolution of bosonic fields is shown to be equivalent to a stochastic trajectory in space-time, corresponding to samples of a statistical mechanical steady-state in a higher dimensional quasi-time. This is proved…
The problem of time evolution in quantum cosmology is studied in the context of a dust-filled, spatially flat Friedmann-Robertson-Walker universe. In this model, two versions of the commonly-adopted notion of internal time can be…
Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which…
Classes of third order non-Abelian evolution equations linked to that of Korteweg-de Vries-type are investigated and their connections represented in a non-commutative B\"acklund chart, generalizing results in [Fuchssteiner B., Carillo S.,…
A quantum-classical limit of the canonical equilibrium time correlation function for a quantum system is derived. The quantum-classical limit for the dynamics is obtained for quantum systems comprising a subsystem of light particles in a…
We develop a new algorithm based on the time-dependent variational principle applied to matrix product states to efficiently simulate the real- and imaginary time dynamics for infinite one-dimensional quantum lattice systems. This…
For the supersymmetric KdV equation, a proper Darboux transformation is presented. This Darboux transformation leads to the B\"{a}cklund transformation found early by Liu and Xie \cite{liu2}. The Darboux transformation and the related…