1

**General Questions and Discussion / MCTDH-X Synopsis**

« **on:**May 09, 2017, 11:49:36 AM »

What MCTDH-X is and what it can do

MCTDH-X is a unique method that -- roughly speaking -- allows one to describe the way little particles behave according to quantum physics. The MCTDH-X software is an implementation of that theory that allows to compute and visualize these quantum dynamics. Specifically, it is a way compute some fundamental properties of ensembles of indistinguishable particles, that is gases of atoms, that are constrained in a box or container at extremely low temperatures or electrons in atoms or molecules.

These properties can be collective, i.e., followed by all (or almost all) particles of the system or not. In the former case one is talking about a Bose-Einstein condensate if the considered particles are indistinguishable bosons or uncorrelated fermions if the considered particles are indistinguishable fermions; in the latter case, the we speak about something more complicated, a so-called fragmented many-boson or a correlated many-fermion state. Indistinguishable bosons at low temperature or indistinguishable electrons in atoms or molecules behave quantum-mechanically: they are wave-like in nature and, hence, totally different than ordinary matter. In a Bose-Einstein condensate (BEC), for instance, all the indistinguishable particles of the gas behave as if they were single effective particle.

Quantum fluctuations and correlations are negligible -- such a behavior is referred to as coherent for bosons and single-configurational for fermions. However, there are many cases in which this not true, even at ultracold temperatures. Phenomena like fragmentation and correlations become very important. In such cases MCTDH-X is applicable, but conventional mean-field descriptions fail. MCTDH-X is designed to solve many-body dynamics of small and intermediate systems of ultracold particles (bosons or fermions) and shed light at phenomena where correlations emerge and mean-field approaches break down.

The fundamental physical equation that governs the evolution of atomic and quantum systems is the Schrödinger equation. MCTDH-X is a method that can, in principle, describe these quantum dynamics exactly, i.e., to any desired given numerical accuracy, for a wide range of scenarios. To see more details about the MCTDH-X method and software, just click here: http://ultracold.org/menu/

MCTDH-X is a unique method that -- roughly speaking -- allows one to describe the way little particles behave according to quantum physics. The MCTDH-X software is an implementation of that theory that allows to compute and visualize these quantum dynamics. Specifically, it is a way compute some fundamental properties of ensembles of indistinguishable particles, that is gases of atoms, that are constrained in a box or container at extremely low temperatures or electrons in atoms or molecules.

These properties can be collective, i.e., followed by all (or almost all) particles of the system or not. In the former case one is talking about a Bose-Einstein condensate if the considered particles are indistinguishable bosons or uncorrelated fermions if the considered particles are indistinguishable fermions; in the latter case, the we speak about something more complicated, a so-called fragmented many-boson or a correlated many-fermion state. Indistinguishable bosons at low temperature or indistinguishable electrons in atoms or molecules behave quantum-mechanically: they are wave-like in nature and, hence, totally different than ordinary matter. In a Bose-Einstein condensate (BEC), for instance, all the indistinguishable particles of the gas behave as if they were single effective particle.

Quantum fluctuations and correlations are negligible -- such a behavior is referred to as coherent for bosons and single-configurational for fermions. However, there are many cases in which this not true, even at ultracold temperatures. Phenomena like fragmentation and correlations become very important. In such cases MCTDH-X is applicable, but conventional mean-field descriptions fail. MCTDH-X is designed to solve many-body dynamics of small and intermediate systems of ultracold particles (bosons or fermions) and shed light at phenomena where correlations emerge and mean-field approaches break down.

The fundamental physical equation that governs the evolution of atomic and quantum systems is the Schrödinger equation. MCTDH-X is a method that can, in principle, describe these quantum dynamics exactly, i.e., to any desired given numerical accuracy, for a wide range of scenarios. To see more details about the MCTDH-X method and software, just click here: http://ultracold.org/menu/