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Sungyun Kim

Publications and source records attributed to Sungyun Kim.

9 recordsLinked to original sources
arXiv2014

Complex spectral analysis and test function spaces

We consider complex eigenstates of unstable Hamiltonian and its physically meaningful regions. Starting from a simple model of a discrete state interacting with a continuum via a general potential, we show that its Lippmann-Schwinger solution set can be decomposed into a free-field set, a set containing lower half plane pole of Green's function and a set containing upper half pole of Green's function. From here distinctive complex eigenstates corresponding to each pole are constructed. We note that on the real line square integrable functions can be decomposed into Hardy class above and below functions which behave well in their respective complex half planes. Test function restriction formulas which remove unphysical growth are given. As a specific example we consider Friedrichs model which solutions and complex eigenstates are known, and compare numerically calculated total time evolution with test function restricted complex eigenstates for various cases. The results shows that test function restricted complex eigenstates capture the essence of decay phenomena quite well.

quant-ph↗
arXiv2011

Decay modes of two repulsively interacting bosons

We study the decay of two repulsively interacting bosons tunneling through a delta potential barrier by direct numerical solution of the time-dependent Schrödinger equation. The solutions are analyzed according to the regions of particle presence: both particles inside the trap (in-in), one particle in and one particle out (in-out), and both particles outside (out-out). It is shown that the in-in probability is dominated by exponential decay, and its decay rate is predicted very well from outgoing boundary conditions. Up to a certain range of interaction strength the decay of in-out probability is dominated by the single particle decay mode. The decay mechanisms are adequately described by simple models.

physics.atom-ph↗
arXiv2009

Computability of entropy and information in classical Hamiltonian systems

We consider the computability of entropy and information in classical Hamiltonian systems. We define the information part and total information capacity part of entropy in classical Hamiltonian systems using relative information under a computable discrete partition. Using a recursively enumerable nonrecursive set it is shown that even though the initial probability distribution, entropy, Hamiltonian and its partial derivatives are computable under a computable partition, the time evolution of its information capacity under the original partition can grow faster than any recursive function. This implies that even though the probability measure and information are conserved in classical Hamiltonian time evolution we might not actually compute the information with respect to the original computable partition.

cond-mat.stat-mech↗
arXiv2008

Undecidability, entropy and information loss in computations of classical physical systems

We investigate how undecidability enters into computations of classical physical systems and contributes to the increase of entropy and loss of information. In actual computation with finite bit of information capacity we accept inconsistency to avoid undecidability, which in turn affects entropy of the system. We apply the Shannon entropy to the discretized Liouvillian system. It is shown that for any finite bit of information capacity information is always lost or the entropy always increases for the probability density following Hamiltonian dynamics, both in time forward and time backward direction, thus showing information theoretical version of second law of thermodynamics. This is due to the finiteness of information capacity and incompressibility of probability distribution in Liouville's equation.

cond-mat.stat-mech↗
arXiv2005

A new way of defining unstable states

We define a new unstable state in the Friedrichs model of a two-level atom. This unstable state is a complex eigenstate of the time evolution operator $\exp(-iHt)$ with a restricted test function space, which is obtained from causality conditions. The unstable state shows exact exponential decay for $t\ge0$. Its emitted field is confined inside the future light-cone. In this way the long-standing problem of exponential catastrophe is removed. This is an example of quantum mechanics outside Hilbert space, which consists of generalized eigenstates in a distribution space, and a dual (test function) space.

physics.atom-ph↗
arXiv2005

Bound states in continuum in an electron waveguide

It is shown that in a double-cavity, two-dimensional electron waveguide, the interplay between quasi-bound states of each cavity leads to the appearance of bound states in continuum for certain distances between the cavities. These bound states may be used to trap electrons in de-localized states distributed in both cavities.

quant-ph↗
arXiv2004

Complex collective states in a one-dimensional two-atom system

We consider a pair of identical two-level atoms interacting with a scalar field in one dimension, separated by a distance $x_{21}$. We restrict our attention to states where one atom is excited and the other is in the ground state, in symmetric or anti-symmetric combinations. We obtain exact collective decaying states, belonging to a complex spectral representation of the Hamiltonian. The imaginary parts of the eigenvalues give the decay rates, and the real parts give the average energy of the collective states. In one dimension there is strong interference between the fields emitted by the atoms, leading to long-range cooperative effects. The decay rates and the energy oscillate with the distance $x_{21}$. Depending on $x_{21}$, the decay rates will either decrease, vanish or increase as compared with the one-atom decay rate. We have sub- and super-radiance at periodic intervals. Our model may be used to study two-cavity electron wave-guides. The vanishing of the collective decay rates then suggests the possibility of obtaining stable configurations, where an electron is trapped inside the two cavities.

quant-ph↗
arXiv2003

Star-unitary transformations. From dynamics to irreversibility and stochastic behavior

We consider a simple model of a classical harmonic oscillator coupled to a field. In standard approaches Langevin-type equations for {\it bare} particles are derived from Hamiltonian dynamics. These equations contain memory terms and are time-reversal invariant. In contrast the phenomenological Langevin equations have no memory terms (they are Markovian equations) and give a time evolution split in two branches (semigroups), each of which breaks time symmetry. A standard approach to bridge dynamics with phenomenology is to consider the Markovian approximation of the former. In this paper we present a formulation in terms of {\it dressed} particles, which gives exact Markovian equations. We formulate dressed particles for Poincaré nonintegrable systems, through an invertible transformation operator $\Lam$ introduced by Prigogine and collaborators. $\Lam$ is obtained by an extension of the canonical (unitary) transformation operator $U$ that eliminates interactions for integrable systems. Our extension is based on the removal of divergences due to Poincaré resonances, which breaks time-symmetry. The unitarity of $U$ is extended to ``star-unitarity'' for $\Lam$. We show that $\Lam$-transformed variables have the same time evolution as stochastic variables obeying Langevin equations, and that $\Lam$-transformed distribution functions satisfy exact Fokker-Planck equations. The effects of Gaussian white noise are obtained by the non-distributive property of $\Lam$ with respect to products of dynamical variables. Therefore our method leads to a direct link between dynamics of Poincaré nonintegrable systems, probability and stochasticity.

cond-mat.stat-mech↗