Related papers: Quantum Brownian oscillator for the stock market

The Brownian motion of a quantum particle in a harmonic confining potential and coupled to a harmonic quantum thermal bath is exactly solvable. It is shown that at low enough temperatures the stationary state is non-Gibbsian due to an…

We develop a hybrid oscillator-qubit processor framework for quantum simulation of strongly correlated fermions and bosons that avoids the boson-to-qubit mapping overhead encountered in qubit hardware. This framework gives exact…

We consider an investor who is dynamically informed about the future evolution of one of the independent Brownian motions driving a stock's price fluctuations. With linear temporary price impact the resulting optimal investment problem with…

Volatility of intra-day stock market indices computed at various time horizons exhibits a scaling behaviour that differs from what would be expected from fractional Brownian motion (fBm). We investigate this anomalous scaling by using…

In this work, we investigate the multimode Brownian oscillators in nonequilibrium scenarios with multiple reservoirs at different temperatures. For this purpose, an algebraic method is proposed. This approach gives the exact time-local…

We develop a quantum embedding method that enables accurate and efficient treatment of interactions between molecules and an environment, while explicitly including many-body correlations. The molecule is composed of classical nuclei and…

We consider quantum Hamiltonian systems composed of mutually interacting "dynamical subsystem" with one or several degrees of freedom and "thermostat" with arbitrary many degrees of freedom, under assumptions that the interaction ensures…

We show how a large family of master equations, describing quantum Brownian motion of a harmonic oscillator with translationally invariant damping, can be derived within a phenomenological approach, based on the assumption that an…

In this article we explore the phenomena of nonequilibrium stochastic process starting from the phenomenological Brownian motion. The essential points are described in terms of Einstein's theory of Brownian motion and then the theory…

We consider a quantum linear oscillator coupled to a bath in equilibrium at an arbitrary temperature and then exposed to an external field arbitrary in form and strength. We then derive the reduced density operator in closed form of the…

Writing the article-Time independent pricing of options in range bound markets; the question in the title came naturally to my mind. It is stated, in the above article, that in certain market conditions the stock price is subjected to an…

We study the quantum version of a simplified model of optimization problems, where quantum fluctuations are introduced by a transverse field acting on the qubits. We find a complex low-energy spectrum of the quantum Hamiltonian,…

Previously only considered a frontier area of Physics, nowadays quantum computing is one of the fastest growing research field, precisely because of its technological applications in optimization problems, machine learning, information…

We investigate the equilibrium properties of a quantum Brownian particle moving in a periodic potential, specifically addressing the nature of the dissipation-driven Schmid transition in the Ohmic regime. By employing World-Line Monte Carlo…

We generalize the classical theory of Brownian motion so as to reckon with non-Markovian effects on both Klein-Kramers and Smoluchowski equations. For a free particle and a harmonic oscillator, it is shown that such non-Markovian effects…

The relativistic quantum dynamics of an electrically charged particle subject to the Klein-Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed:…

It is shown that the recently proposed quantum analogue of classical energy equipartition theorem for two paradigmatic, exactly solved models (i.e., a free Brownian particle and a dissipative harmonic oscillator) also holds true for all…

The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…

Exact quantum master equation for a driven Brownian oscillator system is constructed via a Wigner phase-space Gaussian wave packet approach. The interplay between external field and dissipation leads to this system an effective field…

The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…