Trion Model Research Articles

Positive Trions in InP/ZnSe/ZnS Colloidal Nanocrystals.

InP-based colloidal nanocrystals are being developed as an alternative to cadmium-based materials. However, their optical properties have not been widely studied. In this paper, the fundamental magneto-optical properties of InP/ZnSe/ZnS nanocrystals are investigated at cryogenic temperatures. Ensemble measurements using two-photon excitation spectroscopy revealed the band-edge hole state to have 1Sh symmetry, resolving some controversy on this issue. Single nanocrystal microphotoluminescence measurements provided increased spectral resolution that facilitated direct detection of the lowest energy confined acoustic phonon mode at 0.9 meV, which is several times smaller than the previously reported values for similar nanocrystals. Zeeman splitting of narrow spectral lines in a magnetic field indicated a bright trion emission. A simple trion model was used to identify a positive trion charge. Furthermore, the Zeeman split spectra allowed the direct measurement of both the electron and hole g-factors, which match existing theoretical predictions.

Many-Body Effect on Optical Properties of Monolayer Molybdenum Diselenide.

Excitons in monolayer transition metal dichalcogenides (TMDs) provide a paradigm of composite Boson in a two-dimensional system. This Letter reports a photoluminescence and reflectance study of excitons in monolayer molybdenum diselenide (MoSe2) with electrostatic gating. We observe the repulsive and attractive Fermi polaron modes of the band edge exciton, its excited state, and the spin-off excitons, which the simple three-particle trion model is insufficient to explain. The contrasting energy shift between the exciton and charge-bound excitons (repulsive and attractive polaron modes) and the remarkably different gate dependence of the polaron energy splitting between the ground state and the excited state excitons unambiguously support the Fermi polaron picture for excitons in monolayer TMDs.

Ground and excited state exciton polarons in monolayer MoSe2.

Monolayer transition metal dichalcogenide semiconductors, with versatile experimentally accessible exciton species, offer an interesting platform for investigating the interaction between excitons and a Fermi sea of charges. Using hexagonal boron nitride encapsulated monolayer MoSe2, we study the impact of charge density tuning on the A and B series of exciton Rydberg states, including A:1s, A:2s, B:1s, and B:2s. The doping dependence of the A:2s state provides an opportunity to examine such interactions with greatly reduced exciton binding energy and more spatially diffuse structures, and we found that the impact of the Fermi sea becomes much more dramatic compared to the A:1s state. Using photoluminescence upconversion, we verify that the B:2s exciton state displays similar behavior when interacting with the Fermi sea despite being well above the bare bandgap in energy. Photoluminescence and reflection spectra of the A:1s state show clear evidence that the interaction of the exciton with a Fermi sea is best described by the exciton-polaron model, rather than a trion model. Our experimental results demonstrate that overall features of charge interaction are quite generic and highly robust, offering key insights into the dressed many body states in a Fermi sea.

Magnetoresistance sign change in field-effect transistors via interface doping of Spiro-TAD with F6-TNAP

We report on an organic field-effect transistor with a magnetoresistance (MR) effect whose sign could be tuned by the applied voltage. To realize such a device we doped 2,2′,7,7′-tetrakis-(diphenylamino)-9,9′-spirobifluorene (Spiro-TAD) by inserting a thin layer of 1,3,4,5,7,8-hexafluorotetracyanonapththoquinodimethane (F6-TNAP) deposited between bare SiO2 gate dielectric and Spiro-TAD. Our measurements exhibit two MR components, indicating the coexistence of two underlying mechanisms. The first component with positive MR and a narrow line shape can be ascribed to the bipolaron model. The second component with negative sign and broad line shape can be understood as high-field effect and could be explained by the trion model. The interplay of both MR components results in a voltage-dependent MR with sign change.

Investigating the influence of traps on organic magnetoresistance by molecular doping

Traps are localized, deep lying energetic states and are generally considered detrimental for organic semiconducting devices. In this work, we investigate their influence on the magnetic field sensitive current in organic devices, an effect often called organic magnetoresistance. Polymer thin films were doped with materials well known to influence trap characteristics in such devices. We analyzed the observed trends in the intrinsic magnetic field effects in terms of a trapped trion model, which incorporates the spin dependent formation of excitations at these trap sites. The results provide strong evidence that the intrinsic traps in the polymer material are indeed at the origin of these magnetic field effects. This shows that traps have beneficial properties and that their control may provide an appealing route for the engineering of efficient organic magnetic field sensors.

No Evidence for the Mozart Effect in Children

The Mozart Effect refers to claims that listening to Mozart-like music results in a small, short-lived improvement in spatiotemporal performance. Based on predominantly adult research that has shown equivocal findings, there has been speculation that the Mozart effect may have pedagogical benefits for children. The present study aimed to examine the Mozart effect in children and to evaluate two alternative models proposed to account for the effect, namely the trion model and the arousal-mood model. One hundred and thirty-six Grade 5 students (mean age 10.7 years) were exposed to three experimental listening conditions: Mozart piano sonata K. 448, popular music, and silence. Each condition was followed by a spatiotemporal task, and mood and music questionnaires. The results showed no evidence of a Mozart effect. Speculation about applications of the Mozart effect in children needs to be suspended until an effect can be reliably reproduced.

The Mozart effect: questions about the seminal findings of Rauscher, Shaw, and colleagues.

Seminal evidence for the Mozart effect was presented by Rauscher, Shaw, and colleagues in 1993 and 1994. A critical evaluation of their methodologies and interpretation of findings raises questions that must be answered before this evidence can be regarded as valid. We discuss issues such as their scoring of the Stanford-Binet Intelligence Scale, the experimental design used in their 1993 study, the validity of their 1993 IQ measure, the duration of the Mozart effect, their choice of experimental tasks in relation to predictions of the trion model of neural functioning, and the statistical analyses and interpretation of results in the 1993 and 1994 studies.

Reliable short-term memory in the trion model: toward a cortical language and grammar.

It has previously been shown that Hebb learning in a single column in the trion model of cortical organization occurs by selection. Motivated by von Neumann's solution for obtaining reliability and by models of circulating cortical activity, we introduce Hebb intercolumnar couplings to achieve dramatic enhancements in reliability in the firing of connected columns. In order for these enhancements to occur, specific temporal phase differences must exist between the same inherent spatial-temporal memory patterns in connected columns. We then generalize the criteria of large enhancements in the global firing of the entire connected columnar network to investigate the case when different inherent memory patterns are in the columns. The spatial rotations as well as the temporal phases now are crucial. Only certain combinations of inherent memory patterns meet these criteria with the symmetry properties playing a major role. The columnar order of these memory patterns not in the same symmetry family can be extremely important. This yields the first higher-level architecture of a cortical language and grammar within the trion model. The implications of this result with regard to an innate human language and grammar are discussed.

Music enhances spatial-temporal reasoning: towards a neurophysiological basis using EEG.

Motivated by predictions from the structured trion model of the cortex, based on Mountcastle's columnar organizational principle, behavioral experiments have demonstrated a causal short-term enhancement of spatial-temporal reasoning in college students following listening to a Mozart Sonata (K.448) but not in control conditions. An EEG coherence study reported presence of right frontal and left temporoparietal activity induced by listening to the Mozart Sonata, which carried over into the spatial-temporal tasks in three of the seven subjects. In this paper, we present further predictions from the trion model and discuss how the new SYMMETRIC analysis method can be used in EEG recordings to help determine the neurophysiological basis of specific music enhancing spatial-temporal reasoning. We conclude with potential clinical applications of major significance.

Detecting symmetric patterns in EEG data: a new method of analysis.

Theoretical models of higher cognitive function predict that cortical activity will exhibit families of spatial-temporal patterns of activity whose individual members are related to each other by specific symmetry transformations. In the trion model, it is suggested that these inherent symmetries play a vital role in how we think and reason. We have developed a method of analysis (SYMMETRIC analysis), which detects families of patterns in EEG data, and characterizes the symmetry relationships between members of those pattern families. Using this analysis, significant symmetry families have been found in EEG and single unit spike train data. If symmetry is a crucial aspect of brain function, it is possible that different pathologies are associated with specific types of symmetry relationships in brain activity that could be detected in EEG data by a SYMMETRIC analysis.

Symmetric temporal patterns in cortical spike trains during performance of a short-term memory task

The trion model is a highly structured representation of cortical organizationl which predicts families of symmetric spatial-temporal firing patterns inherent in cortical activity. The symmetries of these inherent firing patterns are used by the brain in short-term memory to perform higher level computations. In the present study, symmetric temporal patterns were searched for in spike trains recorded from cells in parietal cortex of a monkey performing a short-term memory task. A new method of analysis was used to map neuronal firing into sequences of integers representing relative levels of firing rate about the mean (i.e. -1, 0 and 1). The results of this analysis show families of patterns related by symmetry operations. These operations are: i. the interchanging of all the + l’s and -l’s in a given pattern sequence (CT symmetry), ii. the inverting of the temporal sequence of the mapping (T symmetry)1 and iii. the combination of the two previous operations (CT symmetry). Patterns of a given family are found across cells especially in the memory periods of the task; in most cases they reoccur within a given spike train. The pattern families predicted by the model and reported here should be further investigated in multiple microelectrode and EEG recordings. [Neural Res 1997; 19: 509-514]

Persistent patterns of brain activity: An EEG coherence study of the positive effect of music on spatial-temporal reasoning

Motivated by predictions from the structured trion model of the cortex, behavioral experiments have demonstrated a causal short-term enhancement ofspatial-temporal reasoning in college students following exposure to a Mozart sonata, but not in control conditions. The coherence analysis of electroencephalogram (EEG) recordings is well suited to the neurophysiological investigation of this behavioral enhancement. Here we report the presence of right frontal and left temporo-parietal coherent activity induced by listening to Mozart which carried over into the spatial-temporal tasks in three of our seven subjects. This carry-over effect was compared to EEG coherence analysis of spatial-temporal-tasks after listening to text. We suggest that these EEG coherence results provide the beginnings of understanding of the neurophysiological basis of the causal enhancement of spatial-temporal reasoning by listening to specific music. The observed long-lasting coherent fEG pattern might be evidence for structured sequences in cortical dynamics which extend over minutes. Neural Res 1997; 19: 107–116]

Computation by symmetry operations in a structured model of the brain: Recognition of rotational invariance and time reversal.

Symmetries have long been recognized as a vital component of physical and biological systems. What we propose here is that symmetry operations are an important feature of higher brain function and result from the spatial and temporal modularity of the cortex. These symmetry operations arise naturally in the trion model of the cortex. The trion model is a highly structured mathematical realization of the Mountcastle organizational principle [Mountcastle, in The Mindful Brain (MIT, Cambridge, 1978)] in which the cortical column is the basic neural network of the cortex and is comprised of subunit minicolumns, which are idealized as trions with three levels of firing. A columnar network of a small number of trions has a large repertoire of quasistable, periodic spatial-temporal firing magic patterns (MP's), which can be excited. The MP's are related by specific symmetries: Spatial rotation, parity, ``spin'' reversal, and time reversal as well as other ``global'' symmetry operations in this abstract internal language of the brain. These MP's can be readily enhanced (as well as inherent categories of MP's) by only a small change in connection strengths via a Hebb learning rule. Learning introduces small breaking of the symmetries in the connectivities which enables a symmetry in the patterns to be recognized in the Monte Carlo evolution of the MP's. Examples of the recognition of rotational invariance and of a time-reversed pattern are presented. We propose the possibility of building a logic device from the hardware implementation of a higher level architecture of trion cortical columns.

Learning by selection in the trion model of cortical organization.

The basic issue of whether mammalian learning in cortex proceeds via a selection principle, as stressed by Edelman, versus an instructional one is of major importance. We present here a realization of selection learning in the trion model, which is based on the Mountcastle columnar organizational principle of cortex. We suggest that mammalian cortex starts out with an a priori connectivity between minicolumns that is highly structured in time and in space, competing between excitation and inhibition. This provides a "naive" repertoire of spatial-temporal firing patterns that stimuli and internal processing map onto. These patterns can be learned with small modifications to the connectivity strengths determined by a Hebbian learning rule. As various patterns are learned, the repertoire changes somewhat in order to respond properly to various stimuli, but the majority of all possible stimuli still map onto spatial-temporal firing patterns of the original repertoire. In order to show that the example presented here is showing true selectivity and is not an artifact of more stimuli evolving into the learned pattern, we develop a selectivity measure. We suggest that some form of instructional learning (in which connectivities are finely tuned) is present for difficult tasks requiring many trials, whereas very rapid learning involves selectional learning. Both types of learning must be considered to understand behavior.

Reversal of epileptic state by patterned electrical stimulation suggested by trion model calculations.

The trion model is based on the Mountcastle columnar organizational principle of cortex. A trion represents an idealized minicolumn with three levels of firing activity and is highly structured in time and in spatial connections. A network of trions has a large repertoire of quasi-stable, periodic spatial-temporal firing patterns, MPs, which can be excited and each MP can be readily enhanced by a Hebb learning rule. A particular MP present in most repertoires has all trions firing together in synchrony, which we identify as the 'Epileptic' MP (EMP). In trion model simulations, the EMP can be enhanced via the Hebb rule after electrical stimulation so that an epileptic focus with after discharge (about 3-6 Hz) is formed and spontaneous firing of the EMP occurs (as in kindling). Following this, by using a small array of closely-spaced stimulating electrodes out of phase, other MPs are enhanced via the Hebb rule eliminating the dominance of the EMP. We strongly urge that these predictions be tested in the animal models for possible clinical relevance.

Coding of Musical Structure and the Trion Model of Cortex

Guided by the Mountcastle organizational principle for the column as the basic neuronal network in the cortex, we developed the trion model. An essential feature of the model is that it is highly structured in time and in spatial connections. Simulations of a network of trions have shown that large numbers of quasi-stable, periodic spatial-temporal firing patterns can be excited. These patterns can be readily enhanced by only a small change in connection strengths, and the patterns evolve in certain natural sequences from one to another. With only somewhat different parameters than those used for studying memory and pattern recognition, much more flowing and intriguing patterns emerged from the simulations. The results were striking when these probabilistic evolutions were mapped onto pitches and instrument timbres to produce music: For example, different simple mappings of the same evolution give music having the "flavor" of a minuet, a waltz, certain folk music, or styles of specific periods of Western art music. A theme can be learned so that evolutions have this theme and its variations recur. We suggest that we have found a viable cortical model for the coding of certain aspects of musical structure in human composition and perception. Further, we propose that the trion model is relevant for examining creativity in those higher cognitive functions of mathematics and chess that are similar to music.

Music composition and model of cortex

The trion model [PNAS 82, 2364 (1985)] for the firing activity of groups of neurons was developed using the Mountcastle cortical principle of columnar organization; an essential feature is that it is highly structured in time and in spatial connections. The trion model has been shown to be useful for understanding aspects of memory and pattern recognition. To study higher cognitive processes, spatiotemporal firing patterns of time evolutions of the model were mapped onto pitches to produce music. The preliminary results yield the following: (1) The trion music is very pleasant to listen to; (2) one set of connections among the trions produces music sounding like a waltz, and another set gives a minuet; (3) styles of specific periods of composition can be identified. Furthermore. the model demonstrated the ability to learn a musical theme using a Hebbian algorithm. The model provides a window into examining higher brain function.

Associative recall properties of the trion model of cortical organization.

We developed a cooperative model of the cortical column incorporating an idealized subunit, the trion (which represents a localized group of neurons), and a discrete time step for firing. We found that networks composed of a small number of trions (with symmetric interactions) supported up to thousands of quasi-stable, periodic firing patterns (MPs) which could be selected out with only small changes in interaction strengths using a Hebb-type algorithm. Here we report a study of the associative recall properties showing striking features: By considering all possible initial firing patterns (for a given set of network connections), we find 1) It takes on the average only 2-5 time steps to recall an MP. 2) Many of the MPs can be individually accessed by thousands of different initial patterns. The variety of examples presented illustrate the rich, general nature of the model.

Relativistic trion model for hadrons

Relativistic trion model for hadrons

Applications of a unique group embedding of internal symmetry groups andSU(2): spin-extensions for G2 and for the Sp(6)-Trion model

A recently proposed method of embeddingSU (2) and an internal symmetry groupG into a bigger groupG is applied to construct a spin extension ofG2 andSp (6). BecauseG2 andSp (6) possess a generalized quark model the embedding group can be proved to be unique and to be given bySp (14) resp.O (12) forG2 resp.Sp (6). For a particle classification splittings are calculated and tabulated forSp (14) ↓G2 xSU (2) andO (12) ↓Sp (6) xSU (2). The identification of low dimensional irreducible representations ofO (12) is quite satisfactory whereas an unreasonable number of unobserved particles are needed to fill up the supermultiplets of the spin extensionSp (14) of G2.